EUDML

R. Deville and J. Rodríguez proved that, for every Hilbert generated space $X$ , every Pettis integrable function $f : [0, 1] \to X$ is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space $X$ and a scalarly null (hence Pettis integrable) function from $[0, 1]$ into $X$ , which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from $[0, 1]$ (mostly) into $C (K)$ spaces. We focus in more detail on the behavior...

Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss

Marián J. Fabián — 1989

Acta Universitatis Carolinae. Mathematica et Physica

Foreword

Marián J. Fabián — 1998

Acta Universitatis Carolinae. Mathematica et Physica

A generalization of the interior mapping theorem of Clarke and Pourciau

Marián J. Fabián; David Preiss — 1987

Commentationes Mathematicae Universitatis Carolinae

On uniformly Gâteaux smooth $C^{(n)}$ -smooth norms on separable Banach spaces

Marián J. Fabián; Václav Zizler — 1999

Czechoslovak Mathematical Journal

Every separable Banach space with $C^{(n)}$ -smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and $C^{(n)}$ -smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.

Foreword

Marián J. Fabián; Václav Zizler; Bohuslav Balcar — 2000

Acta Universitatis Carolinae. Mathematica et Physica

A note on lattice renormings

Marián J. Fabián; Petr Hájek; Václav Zizler — 1997

Commentationes Mathematicae Universitatis Carolinae

It is shown that every strongly lattice norm on $c_{0} (Γ)$ can be approximated by $C^{\infty}$ smooth norms. We also show that there is no lattice and Gâteaux differentiable norm on $C_{0} [0, ω_{1}]$ .

Remarks on continuous images of Radon-Nikodým compacta

Marián J. Fabián; Martin Heisler; Eva Matoušková — 1998

Commentationes Mathematicae Universitatis Carolinae

A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact $K$ we prove: If $K$ is totally disconnected, then it is Radon-Nikod’ym compact. If $K$ is adequate, then it is even Eberlein compact.

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Concerning interior mapping theorem

Once more on continuity of maximal monotone mappings

On singlevaluedness and (strong) upper semicontinuity of maximal monotone mappings

Theory of Fréchet cones

Concerning a geometrical characterization of Fréchet differentiability

On coincidence of Pettis and McShane integrability

Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss

Foreword

A generalization of the interior mapping theorem of Clarke and Pourciau

On uniformly Gâteaux smooth $C^{(n)}$ -smooth norms on separable Banach spaces

Foreword

A note on lattice renormings

Remarks on continuous images of Radon-Nikodým compacta