Faculty of Mathematics and Physics

Seigneur, ouvre mes lèvres,
et ma bouche publiera ta louange.
Psaume 51

Research papers

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Finitely additive measures and complementability of Lipschitz-free spaces (with M.Cúth and P.Kaplický; Preprint no. MATH-KMA-2017/537, see KMA Preprint Series; http://arxiv.org/abs/1703.08384)

Absolute Fσδ spaces (with V.Kovařík; http://arxiv.org/abs/1703.03066)

Isometric representation of Lipschitz-free spaces over convex domains in finite-dimensional spaces (with M.Cúth and P.Kaplický; Mathematika 63 (2017), no. 2, 538-552; doi:10.1112/S0025579317000031; Preprint no. MATH-KMA-2016/529; http://arxiv.org/abs/1610.03966)

Preduals of JBW* triples are 1-Plichko spaces (with M.Bohata, J.Hamhalter, A.M.Peralta and H.Pfitzner; Preprint no. MATH-KMA-2016/527, see KMA Preprint Series; http://arxiv.org/abs/1609.00274)

On projectional skeletons in Vašák spaces (Comment. Math. Univ. Carolinae 58 (2017), no. 2, 173-182; doi:10.14712/1213-7243.2015.200; Preprint no. MATH-KMA-2015/513;http://arxiv.org/abs/1602.02558)

Decompositions of preduals of JBW and JBW* algebras (with M.Bohata and J.Hamhalter; J. Math. Anal. Appl. 446 (2017), no. 1, 18–37; doi:10.1016/j.jmaa.2016.08.031; Preprint no. MATH-KMA-2015/504; http://arxiv.org/abs/1511.01086)

On Markushevich bases in preduals of von Neumann algebras (with M.Bohata and J.Hamhalter; Israel J. Math. 214 (2016), no. 2, 867–884; doi:10.1007/s11856-016-1365-y; Preprint no. MATH-KMA-2015/493; http://arxiv.org/abs/1504.06981)

Preserving affine Baire classes by perfect affine maps (with J.Spurný; Quaest. Math. 39 (2016), no. 3, 351-362; doi:10.2989/16073606.2015.1073813; Preprint no. MATH-KMA-2015/486; http://arxiv.org/abs/1501.05118)

Baire classes of affine vector-valued functions (with J.Spurný; Studia Math. 233 (2016), no. 3, 227-277; doi:10.4064/sm8278-5-2016; Preprint no. MATH-KMA-2014/475; http://arxiv.org/abs/1411.1874)

Quantification of the Banach-Saks property (with H.Bendová and J.Spurný; J. Funct. Anal. 268 (2015), no. 7, 1733-1754; doi:10.1016/j.jfa.2014.12.003; Preprint no. MATH-KMA-2014/467; http://arxiv.org/abs/1406.0684)

Monotone retractability and retractional skeletons (with M.Cúth; J. Math. Anal. Appl. 423 (2015), no. 1, 18–31; doi:10.1016/j.jmaa.2014.09.029; Preprint no. MATH-KMA-2014/455; http://arxiv.org/abs/1403.4480)

Typical martingale diverges at a typical point (with J.Spurný; J. Theor. Prob. 29 (2016), no. 1, 180-205; doi:10.1007/s10959-014-0567-7; Preprint no. MATH-KMA-2013/445; http://arxiv.org/abs/1311.0194)

Rich families and elementary submodels (with M.Cúth; Cent. Eur. J. Math. 12 (2014), no. 7, 1026-1039, doi:10.2478/s11533-013-0400-z; Preprint no. MATH-KMA-2013/428; http://arxiv.org/abs/1308.1818)

Note on Bessaga-Klee classification (with M.Cúth; Colloq. Math. 140 (2015), no. 1, 59-74; doi:10.4064/cm140-1-5; Preprint no. MATH-KMA-2013/426; http://arxiv.org/abs/1307.8246)

On quantitative Schur and Dunford-Pettis properties (with J.Spurný; Bull. Austral. Math. Soc. 91 (2015), no. 3, 471-486; doi:10.1017/S0004972715000076; Preprint no. MATH-KMA-2013/415; http://arxiv.org/abs/1302.6369)

Optimal approximate fixed point results in locally convex spaces (with C.S.Barroso and M.P.Rebouças; J. Math. Anal. Appl. 401 (2013), no. 1, 1-8; doi:10.1016/j.jmaa.2012.10.026; Preprint no. MATH-KMA-2012/395; http://arxiv.org/abs/1206.3544)

Quantification of the reciprocal Dunford-Pettis property (with J.Spurný; Studia Math. 210 (2012), no. 3, 261-278, doi:10.4064/sm210-3-6; Preprint no. MATH-KMA-2012/391; http://arxiv.org/abs/1204.4308)

Quantitative Dunford-Pettis property (with M.Kačena and J.Spurný; Advances in Math. 234 (2013), 488-527, doi:10.1016/j.aim.2012.10.019; Preprint no. MATH-KMA-2011/377; http://arxiv.org/abs/1110.1243)

Complementation in spaces of continuous functions on compact lines (with W.Kubiś; J. Math. Anal. Appl. 386 (2012), no. 1, 241-257; doi:10.1016/j.jmaa.2011.07.057; Preprint no. MATH-KMA-2011/363; http://arxiv.org/abs/1105.4262)

On a difference between quantitative weak sequential completeness and the quantitative Schur property (with J.Spurný; Proc. Amer. Math. Soc. 140 (2012), no. 10, 3435-3444; doi:10.1090/S0002-9939-2012-11175-X; Preprint no. MATH-KMA-2011/359; http://arxiv.org/abs/1103.2975)

On the approximate fixed point property in abstract spaces (with C.S.Barroso and P-K.Lin; Math. Z. 271 (2012), no. 3-4, 1271-1285; doi:10.1007/s00209-011-0915-6; Preprint no. MATH-KMA-2011/357; http://arxiv.org/abs/1101.5274)

On quantification of weak sequential completeness (with H.Pfitzner and J.Spurný; J. Funct. Anal. 260 (2011), no. 10, 2986-2996, doi:10.1016/j.jfa.2011.02.006; Preprint no. MATH-KMA-2010/352; http://arxiv.org/abs/1011.6553)

A quantitative version of James' compactness theorem (with B.Cascales and J.Spurný; Proc. Edinburgh Math. Soc., II. Ser. 55 (2012), no. 2, 369-386, doi:10.1017/S0013091510000842; Preprint no. MATH-KMA-2010/334; http://arxiv.org/abs/1005.5693)

Spaces not containing l1 have weak aproximate fixed point property (J. Math. Anal. Appl. 373 (2011), no. 1, 134-137, doi:10.1016/j.jmaa.2010.06.052; Preprint no. MATH-KMA-2010/331; http://arxiv.org/abs/1005.1218)

Compactness in Banach space theory - selected problems (with A.Avilés; Preprint no. MATH-KMA-2009/314; Rev. R. Acad. Cien. Serie A. Mat. 104 (2010), no. 2, 337-352, DOI: 10.5052/RACSAM.2010.21; http://arxiv.org/abs/1005.4303)

Envelopes of open sets and extending holomorphic functions on dual Banach spaces (with D.García and M.Maestre; J. Math. Anal. Appl. 363 (2010), no. 2, 663-678; doi:10.1016/j.jmaa.2009.09.051; Preprint no. MATH-KMA-2009/306; http://arxiv.org/abs/0905.2531)

A note on intersections of simplices (with D.A.Edwards and J.Spurný; Bull. Soc. Math. France 139 (2011), no. 1, 89-95; Preprint no. MATH-KMA-2009/304)

The structure of Valdivia compact lines (with W.Kubiś Topol. Appl. 157 (2010), no. 7, 1142-1151; doi:10.1016/j.topol.2010.02.001; Preprint no. MATH-KMA-2008/284; http://arxiv.org/abs/0811.4144)

Boundaries of compact convex sets and fragmentability (with J.Spurný; J. Funct. Anal. 256 (2009), no. 3, 865-880; doi:10.1016/j.jfa.2008.11.004; Preprint no. MATH-KMA-2008/262)

Natural examples of Valdivia compact spaces (Preprint no. MATH-KMA-2007/247; J. Math. Anal. Appl. 340 (2008), no. 1, 81-101; doi:10.1016/j.jmaa.2007.07.069)

Quotients of continuous convex functions on nonreflexive Banach spaces (with P.Holický, L.Veselý and L.Zajíček; Preprint no. MATH-KMA-2007/241; Bull. Acad. Polon. Sci. 55 (2007), no. 3, 211-217.)

On products with the unit interval (Preprint no. MATH-KMA-2007/233; Topol. Appl. 155 (2008), no. 10, 1098-1104; doi:10.1016/j.topol.2008.01.010)

Fiber orders and compact spaces of uncountable weight (with A.Avilés; Fundamenta Mathematicae 204 (2009), no. 1, 7-38; doi:10.4064/fm204-1-2; Preprint no. MATH-KMA-2006/227; http://arxiv.org/abs/0903.0657)

(I)-envelopes of unit balls and James' characterization of reflexivity (Preprint no. MATH-KMA-2006/202; Studia Math. 182 (2007), no. 1, 29-40.)

The convergence space of minimal usco mappings (with R.Anguelov; Preprint no. MATH-KMA-2006/197; Czechoslovak Math. J. 59 (134) (2009), no. 1, 101-128; doi:10.1007/s10587-009-0008-4)

Baire-one mappings contained in a usco map (Preprint no. MATH-KMA-2006/196; Comment. Math. Univ. Carolinae 48 (2007), no. 1, 135-145.)

(I)-envelopes of closed convex sets in Banach spaces (Preprint no. MATH-KMA-2006/191; Israel J. Math. 162 (2007), no. 1, 157-181.)

A converse to Amir-Lindenstrauss theorem in complex Banach spaces (Preprint no. MATH-KMA-2006/190; Rev. R. Acad. Cien. Serie A. Mat. 100 (2006), no. 1-2, 183-190.)

Complex Banach spaces with Valdivia dual unit ball ( Extracta Math. 20 (2005), no.3, 243-259; Preprint no. MATH-KMA-2005/187)

C(K) spaces which cannot be uniformly embedded into $c_0(\Gamma)$ (with J.Pelant and P.Holický, Fundamenta Mathematicae 192 (2006), 245-254; Preprint no. MATH-KMA-2005/174)

Descriptive hierarchy of complex Banach spaces, Spring 2005, unpublished manuscript - pdf file (237 kB); Preprint no. MATH-KMA-2005/169, see KMA Preprint Series

A solution of the abstract Dirichlet problem for Baire-one functions (with J.Spurný; J. Funct. Anal. 232 (2006), 259-294; Preprint no. MATH-KMA-2005/167)

Remark on the abstract Dirichlet problem for Baire-one functions (Preprint no. MATH-KMA-2004/143, Bull. Acad. Polon. Sci. 53 (2005), no. 1, 55-73.)

Extending Baire-one functions on topological spaces (with J.Spurný;Topol. Appl. 149 (2005), 195-216; Preprint no. MATH-KMA-2004/133)

Note on Countable Unions of Corson Countably Compact Spaces (Preprint No. MATH-KMA-2003/113; Comment. Math. Univ. Carolinae 45 (2004), no. 3, 499-507)

Descriptive Properties of Spaces of Signed Measures (with M.Raja; Preprint No. MATH-KMA-2003/109, Acta Univ. Carolinae 44 (2003), no. 2, 79-88)

Filling Analytic Sets by the Derivatives of C1-Smooth Bumps (with M.Fabian and J.Kolář; Preprint No. MATH-KMA-2002/76; Proc. Amer. Math. Soc. 133 (2005), no. 1, 295-303)

On the Class of Continuous Images of Valdivia Compacta (Preprint No. MATH-KMA-2002/75; Extracta Math. 18 (2003), no.1, 65-80)

On Subclasses of Weak Asplund Spaces (with K.Kunen, Preprint No. MATH-KMA-2001/62; Proc. Amer. Math. Soc. 133 (2005), no.2, 425-429)

A Weak Asplund Spaces Whose Dual is not in Stegall's Class (Preprint No. MATH-KMA-2001/59, Proc. Amer. Math. Soc. 130 (2002), no. 7, 2139-2143)

M-bases in Spaces of Continuous Functions on Ordinals (Preprint No. MATH-KMA-2001/55; Colloquium Math. 92 (2002), no. 2, 179-187)

A New Banach Space with Valdivia Dual Unit Ball (Preprint No. MATH-KMA-2001/46; Israel J. Math. 131 (2002), 139-147)

Note on Markushevich Bases in Subspaces and Quotients of Banach Spaces (Preprint No. MATH-KMA-2000/39; Bull. Acad. Polon. Sci. 50 (2002), no. 2, 117-126)

A Characterization of Weakly Lindelöf Determined Banach Spaces (Preprint No. KMA-2000-29; Serdica Math. J. 29 (2003), no. 2, 95-108)

On Double-derived Sets in Topological Spaces (Houston Journal of Mathematics 26 (2000), no. 4, 807-809)

Valdivia Compact Spaces in Topology and Banach Space Theory (a survey paper, Extracta Math. 15, no.1, 2000, 1-85)

Valdivia Compacta and Biduals of Asplund Spaces (Preprint No. KMA-1999-14; in T.Banakh (ed.), `General Topology in Banach spaces', Nova Sci. Publ., Huntington, New York, 2001, 115-125)

Valdivia Compacta and Subspaces of C(K) Spaces (Preprint No. KMA-1999-12; Extracta Math. 14, no. 3(1999), 355-371)

Embedding the Ordinal Segment$[0,\omega_1]$ into Continuous Images of Valdivia Compacta (Preprint No. KMA-1999-3; Comment. Math. Univ. Carolinae 40, no. 4, (1999), 777-783)

Valdivia Compacta and Equivalent Norms (Preprint No. KMA-1999-2; Studia Mathematica 138, no. 2, (2000), 179-191)

A Characterization of Valdivia Compact Spaces (Collectanea Mathematica 51, no. 1,(2000), 59-81)

Continuous Images and Other Topological Properties of Valdivia Compacta ( Fundamenta Mathematicae 162 (1999), no.2, 181-192)

An Example Concerning Valdivia Compact Spaces ( Serdica Math. J., 25 (2) (1999), 131-140)

Descriptive Properties of Spaces of Measures (with P.Holický, Bull. Acad. Polon. Sci., 47 (1) (1999), 37-51)

Weakly Stegall spaces, Spring 1997, unpublished manuscript - pdf file (99 kB)

Stegall Compact Spaces which are not Fragmentable(Topol. Appl., 96 (2) (1999), 121-132)

New Examples of Hereditarily t-Baire Spaces ( Bull. Acad. Polon. Sci., 46 (2) (1998), 197-210)

Note on Connections of the Point of Continuity Property and Kuratowski Problem on Function Having the Baire Property (Acta Univ. Carolinae, 38 (1) (1997), 3-12)

Remark on the Point of Continuity Property II (with P.Holický, Bull. Acad. Polon. Sci., 43 (2) (1995), 105-111)

Abstract

Complementation in spaces of continuous functions on compact lines
We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings of the separable complementation property in spaces of continuous functions on compact lines. These properties include in particular continuous separable complementation property and existence of a projectional skeleton.

Theses

Compact spaces and their applications in Banach space theory (Doctoral (DSc.) Thesis, 2011)

Abstract of the thesis ("teze") (389 kB)

Article on the topic of the thesis (in Czech; Akademický bulletin 6/2012, p. 23)



Contents:
  1. Introduction
  2. Weak Asplund spaces and their subclasses
  3. Valdivia compact spaces

The introductory chapter together with bibliography is contained in this pdf file (374 kB). Chapter 2 consists of three papers and one preprint from the above list. Chapter 3 consists of another four papers from the above list.

Classes of compact spaces in functional analysis (Habilitation Thesis, MFF UK, 2004)

Contents:
  • Preface
  • Introduction
  • Valdivia compacta and continuous images
  • Markushevich bases and primarily Lindelöf spaces
  • Valdivia type Banach spaces
  • Bibliography

Preface, Introduction, the introductory notes to the remaining chapters and Bibliography are contained in this pdf file (297 kB). Except for this the thesis contains six published papers from the above list.

Continuity-like Properties of Mappings (PhD Thesis, MFF UK 1997)

Abstract of the thesis ("autoreferát") (143 kB)

Contents:
  • Introduction - pdf file (58 kB)
  • Remark on the Point of Continuity Property II (a published joint paper with P.Holický, see above)
  • Note on Connections of Point of Continuity Property and Kuratowski Problem on Function Having the Baire Property (a published paper, see above)
  • New Examples of Hereditarily t-Baire Spaces (a published paper, see above)
  • Stegall Compact Spaces Which Are Not Fragmentable (a published paper, see above)
  • Few remarks on structure of certain spaces of measures - pdf file (209 kB)


Dědičně Baireovy prostory a vlastnost bodu spojitosti (Hereditarily Baire Spaces and Point of Continuity Property, in Czech) (Diplomová práce - Master Thesis, MFF UK 1995, pdf file (429 kB))