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The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.

Setkání s profesorem Gustavem Choquetem

Mirko Rokyta (1992)

Pokroky matematiky, fyziky a astronomie

Sets in which the Besov norm in attained.

Arzolay, Wilmer, Ramos-Fernández, Julio C. (2004)

Boletín de la Asociación Matemática Venezolana

Sets invariant under projections onto one dimensional subspaces

Simon Fitzpatrick, Bruce Calvert (1991)

Commentationes Mathematicae Universitatis Carolinae

The Hahn–Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$ , and $B$ is a circled convex body in $E$ , there is a continuous linear projection $P$ onto $m$ with $P (B) \subseteq B$ . We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement.

Sets invariant under projections onto two dimensional subspaces

Simon Fitzpatrick, Bruce Calvert (1991)

Commentationes Mathematicae Universitatis Carolinae

The Blaschke–Kakutani result characterizes inner product spaces $E$ , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace $F$ there is a norm 1 linear projection onto $F$ . In this paper, we determine which closed neighborhoods $B$ of zero in a real locally convex space $E$ of dimension at least 3 have the property that for every 2 dimensional subspace $F$ there is a continuous linear projection $P$ onto $F$ with $P (B) \subseteq B$ .

Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions

Paweł Domański, Mikael Lindström (2002)

Annales Polonici Mathematici

We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.

Sets of interpolation for Fourier transforms of bimeasures

Colin C. Graham, Bertram M. Schreiber (1987)

Colloquium Mathematicae

Sets of minimal points in L...(...0,1..., dt).

Jan-Ove Larsson (1988)

Mathematica Scandinavica

Sets of simple observables in the operational approach to quantum theory

C. M. Edwards (1971)

Annales de l'I.H.P. Physique théorique

Sets with the Radon-Nikodým property in conjugate Banach space

J. Bourgain (1980)

Studia Mathematica

Set-valued mappings and structure of Banach spaces

Kolomý, Josef (1987)

Proceedings of the 14th Winter School on Abstract Analysis

Seventy years of Professor Vlastimil Pták: biography and interview

Zdeněk Vavřín (1996)

Mathematica Bohemica

Several characterizations for the special atom spaces with applications.

Geraldo Soares de Souza, Richard O'Neil, Gary Sampson (1986)

Revista Matemática Iberoamericana

The theory of functions plays an important role in harmonic analysis. Because of this, it turns out that some spaces of analytic functions have been studied extensively, such as Hp-spaces, Bergman spaces, etc. One of the major insights that has developed in the study of Hp-spaces is what we call the real atomic characterization of these spaces.

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