Schauder bases for symmetric tensor products

Bogdan C. Grecu; Raymond A. Ryan

doi:10.2977/prims/1145475364

Schauder bases for symmetric tensor products

Bogdan C. Grecu, Raymond A. Ryan

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

12 Citations (Scopus)

Abstract

For a Danach space E with Schauder basis, we prove that the n fold symmetric tensor product ⊗̂_μⁿ, _sE has a Schauder basis for all symmetric uniform crossnorms μ. This is done by modifying the square ordering on ℕⁿ and showing that the new ordering gives tensor product bases in both ⊗̂ _μⁿE and ⊗̂_μⁿ, _sE.

Original language	English
Pages (from-to)	459-469
Number of pages	11
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	41
Issue number	2
DOIs	https://doi.org/10.2977/prims/1145475364
Publication status	Published - Jul 2005

Keywords

Schauder basis
Tensor product

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10.2977/prims/1145475364

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title = "Schauder bases for symmetric tensor products",

abstract = "For a Danach space E with Schauder basis, we prove that the n fold symmetric tensor product {\^⊗}μn, sE has a Schauder basis for all symmetric uniform crossnorms μ. This is done by modifying the square ordering on ℕn and showing that the new ordering gives tensor product bases in both {\^⊗} μnE and {\^⊗}μn, sE.",

keywords = "Schauder basis, Tensor product",

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year = "2005",

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AU - Grecu, Bogdan C.

AU - Ryan, Raymond A.

PY - 2005/7

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AB - For a Danach space E with Schauder basis, we prove that the n fold symmetric tensor product ⊗̂μn, sE has a Schauder basis for all symmetric uniform crossnorms μ. This is done by modifying the square ordering on ℕn and showing that the new ordering gives tensor product bases in both ⊗̂ μnE and ⊗̂μn, sE.

KW - Schauder basis

KW - Tensor product

UR - https://www.scopus.com/pages/publications/24944454596

U2 - 10.2977/prims/1145475364

DO - 10.2977/prims/1145475364

M3 - Article

SN - 0034-5318

VL - 41

SP - 459

EP - 469

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 2

ER -

Schauder bases for symmetric tensor products

Abstract

Keywords

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