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Concerning entire functions in B 0 -algebras

W. Żelazko (1994)

Studia Mathematica

We construct a non-m-convex non-commutative B 0 -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

Concerning weak * -extreme points

Eva Matoušková (1995)

Commentationes Mathematicae Universitatis Carolinae

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak * -extreme points of the unit ball is discrete.

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , ν ) . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja (2015)

Studia Mathematica

We show that in a super-reflexive Banach space, the conditionality constants k N ( ) of a quasi-greedy basis ℬ grow at most like O ( ( l o g N ) 1 - ε ) for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in L p for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with k N ( ) l o g N .

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