Displaying similar documents to “On the Riesz-Fischer theorem in a smooth Banach space”

Banach spaces which embed into their dual

Valerio Capraro, Stefano Rossi (2011)

Colloquium Mathematicae

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We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz representation theorem.

On the Kleinecke-Shirokov Theorem for families of derivations

Victor S. Shulman, Yuriĭ V. Turovskii (2002)

Studia Mathematica

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It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.

A note on Riesz spaces with property- b

Ş. Alpay, B. Altin, C. Tonyali (2006)

Czechoslovak Mathematical Journal

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We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.

Acknowledgement of priority: Separable quotients of Banach spaces.

Marek Wójtowicz (1998)

Collectanea Mathematica

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In previous papers, it is proved, among other things, that every infinite dimensional sigma-Dedekind complete Banach lattice has a separable quotient. It has come to my attention that L. Weis proved this result without assuming sigma-Dedekind completeness; the proof is based, however, on the deep theorem of J. Hagler and W.B. Johnson concerning the structure of dual balls of Banach spaces and therefore cannot be applied simply to the case of locally convex solid topologically complete...

F. Riesz Theorem

Keiko Narita, Kazuhisa Nakasho, Yasunari Shidama (2017)

Formalized Mathematics

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In this article, we formalize in the Mizar system [1, 4] the F. Riesz theorem. In the first section, we defined Mizar functor ClstoCmp, compact topological spaces as closed interval subset of real numbers. Then using the former definition and referring to the article [10] and the article [5], we defined the normed spaces of continuous functions on closed interval subset of real numbers, and defined the normed spaces of bounded functions on closed interval subset of real numbers. We also...

An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

Alistair Bird, Niels Jakob Laustsen (2010)

Banach Center Publications

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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...