Bounded factorization property for Fréchet spaces
An operator T ∈ L(E, F) factors over G if T = RS for some S ∈ L(E, G) and R ∈ L(G, F); the set of such operators is denoted by LG(E, F). A triple (E, G, F) satisfies bounded factorization property (shortly, (E, G, F) ∈ ℬ︁ℱ) if LG(E, F) ⊂ LB(E, F), where LB(E, F) is the set of all bounded linear oper...
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Published in | Mathematische Nachrichten Vol. 253; no. 1; pp. 81 - 91 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Berlin
WILEY-VCH Verlag
01.05.2003
WILEY‐VCH Verlag |
Subjects | |
Online Access | Get full text |
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Summary: | An operator T ∈ L(E, F) factors over G if T = RS for some S ∈ L(E, G) and R ∈ L(G, F); the set of such operators is denoted by LG(E, F). A triple (E, G, F) satisfies bounded factorization property (shortly, (E, G, F) ∈ ℬ︁ℱ) if LG(E, F) ⊂ LB(E, F), where LB(E, F) is the set of all bounded linear operators from E to F. The relationship (E, G, F) ∈ ℬ︁ℱ is characterized in the spirit of Vogt's characterisation of the relationship L(E, F) = LB(E, F) [23]. For triples of K�othe spaces the property ℬ︁ℱ is characterized in terms of their K�othe matrices.
As an application we prove that in certain cases the relations L(E, G1) = LB(E, G1) and L(G2, F) = LB(G2, F) imply (E, G, F) ∈ ℬ︁ℱ where G is a tensor product of G1 and G2. |
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Bibliography: | ArticleID:MANA#200310046 ark:/67375/WNG-3BRBHT6R-M istex:7B10EA29CA665D9AED8CF0876962EEEDD763B1C7 Phone: 90 216 4839033, Fax: 90 216 4839013 |
ISSN: | 0025-584X 1522-2616 |
DOI: | 10.1002/mana.200310046 |