Results 231 to 240 of about 155,050 (273)
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Banach Frames for Conjugate Banach Spaces
Zeitschrift für Analysis und ihre Anwendungen, 2004Retro Banach frames for conjugate Banach spaces have been introduced and studied. It has been proved that a Banach space E is separable if and only if E* has a retro Banach frame. Finally, a necessary and sufficient condition for a sequence in a separable Banach space to be a retro Banach frame has been given.
Jain, P. K. +2 more
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Russian Mathematical Surveys, 1966
CONTENTSIntroduction § 1. Scales of Banach spaces § 2. Normal embeddings of spaces and of their duals § 3. Normal scale of spaces. Related spaces § 4. Interpolation properties. Minimal and maximal scales § 5. The Holder scale § 6. The Marcinkiewicz scale § 7. Analytic scales § 8. Spaces of means § 9. Hilbert scalesAddendum: Yu. I. Petunin. A non-linear
Kreĭn, S. G., Petunin, Yu. I.
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CONTENTSIntroduction § 1. Scales of Banach spaces § 2. Normal embeddings of spaces and of their duals § 3. Normal scale of spaces. Related spaces § 4. Interpolation properties. Minimal and maximal scales § 5. The Holder scale § 6. The Marcinkiewicz scale § 7. Analytic scales § 8. Spaces of means § 9. Hilbert scalesAddendum: Yu. I. Petunin. A non-linear
Kreĭn, S. G., Petunin, Yu. I.
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ON BI-BANACH FRAMES IN BANACH SPACES
International Journal of Wavelets, Multiresolution and Information Processing, 2014Bi-Banach frames in Banach spaces have been defined and studied. A necessary and sufficient condition under which a Banach space has a Bi-Banach frame has been given. Finally, Pseudo exact retro Banach frames have been defined and studied.
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Totally Incomparable Banach Spaces and Three‐Space Banach Space Ideals
Mathematische Nachrichten, 1987AbstractIn this paper we present four methods to generate three‐space BANACH space ideals. They are based on the concept of total incomparability of H. P. ROSENTHAL and on a dual concept, total coincomparability, which is here introduced. We use the assertion that the sum of two totally incomparable closed subspaces of a BANACH space is norm‐closed ...
Alvarez, Teresa +2 more
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Banach Spaces and Banach Lattices
2016We shall now give some background in the theory of normed and Banach spaces, including the key definitions of dual and bidual spaces and of an isomorphism and an isometric isomorphism between two normed spaces. In particular, we shall show how certain bidual spaces can be embedded in other Banach spaces.
H. G. Dales +3 more
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A Banach Space of Distributions (I)
Journal of the London Mathematical Society, 1957Soit \(L\) l'espace des fonctions \(f\) sommables sur un intervalle \(I = [0, c]\), muni de sa norme usuelle, \(\Vert f\Vert = \int_0^c \vert f\vert\,dx\). Posons \(L_k = D^k L\), avec la topologie image de \(0\) de \(L\) par \(D^k\); \((D\) opérateur de dérivation). Il résulte immédiatement de ce que le rapporteur a établi en 1954 [Rend. Mat. Appl. 14,
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2021
Abstract The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem.
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Abstract The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem.
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Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces
2016This paper is a survey on the Hyers–Ulam stability of additive functional inequalities, quadratic functional inequalities, additive ρ-functional inequalities, and quadratic ρ-functional inequalities in Banach spaces and fuzzy Banach spaces. Its content is divided into the following sections: 1. Introduction and Preliminaries.
Choonkil Park +2 more
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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