Basic sequences, embeddings, and the uniqueness of the symmetric structure in unitary matrix spaces

Jonathan Arazy

doi:10.1016/0022-1236(81)90052-5

Basic sequences, embeddings, and the uniqueness of the symmetric structure in unitary matrix spaces

Research output: Contribution to journal › Article › peer-review

Abstract

For every symmetric sequence space E we denote by C_E the associated unitary matrix space. We show that every basic sequence in C_E has a subsequence which embeds in l₂ ⊕ E. This reduces many problems about C_E to the analogous problems on E. We also study the asymptotic behavior of the embeddings of one unitary sequence space into another, and the problem of the uniqueness of the symmetric structure of unitary matrix spaces.

Original language	English
Pages (from-to)	302-340
Number of pages	39
Journal	Journal of Functional Analysis
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/0022-1236(81)90052-5
State	Published - 15 Feb 1981
Externally published	Yes

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(81)90052-5

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abstract = "For every symmetric sequence space E we denote by CE the associated unitary matrix space. We show that every basic sequence in CE has a subsequence which embeds in l2 ⊕ E. This reduces many problems about CE to the analogous problems on E. We also study the asymptotic behavior of the embeddings of one unitary sequence space into another, and the problem of the uniqueness of the symmetric structure of unitary matrix spaces.",

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AB - For every symmetric sequence space E we denote by CE the associated unitary matrix space. We show that every basic sequence in CE has a subsequence which embeds in l2 ⊕ E. This reduces many problems about CE to the analogous problems on E. We also study the asymptotic behavior of the embeddings of one unitary sequence space into another, and the problem of the uniqueness of the symmetric structure of unitary matrix spaces.

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Basic sequences, embeddings, and the uniqueness of the symmetric structure in unitary matrix spaces

Abstract

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