Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1]d

Fernando Albiac; José Luis Ansorena

doi:10.1002/mana.201600236

Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1]d

Mathematische Nachrichten ◽

10.1002/mana.201600236 ◽

2016 ◽

Vol 290 (8-9) ◽

pp. 1177-1186 ◽

Cited By ~ 1

Author(s):

Fernando Albiac ◽

José Luis Ansorena

Keyword(s):

Besov Spaces ◽

Sequence Spaces ◽

Mixed Sequence ◽

Isomorphic Classification

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The isomorphic classification of Besov spaces over $\mathbb{R}^{d}$ revisited

Banach Journal of Mathematical Analysis ◽

10.1215/17358787-3336542 ◽

2016 ◽

Vol 10 (1) ◽

pp. 108-119 ◽

Cited By ~ 2

Author(s):

Fernando Albiac ◽

José Luis Ansorena

Keyword(s):

Besov Spaces ◽

Isomorphic Classification

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Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500015341 ◽

1981 ◽

Vol 90 (1-2) ◽

pp. 63-70 ◽

Cited By ~ 5

Author(s):

Bernd Carl

Keyword(s):

Banach Space ◽

Asymptotic Behaviour ◽

Besov Spaces ◽

Eigenvalue Problems ◽

Function Spaces ◽

Sequence Spaces ◽

Entropy Numbers ◽

Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

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