NDLI: On stably -monotone Banach couples

Content Provider	Springer Nature Link
Author	Astashkin, S. V. Tikhomirov, K. E.
Copyright Year	2010
Abstract	The -monotonicity of Banach couples which is stable with respect to multiplication of weight by a constant is studied. Suppose that E is a separable Banach lattice of two-sided sequences of reals such that ‖e n‖ = 1 (n ∈ ℕ), where e n n ∈ℤ is the canonical basis. It is shown that $$ \vec E $$ = (E, E(2-k )) is a stably -monotone couple if and only if $$ \vec E $$ is -monotone and E is shift-invariant. A non-trivial example of a shift-invariant separable Banach lattice E such that the couple $$ \vec E $$ is -monotone is constructed. This result contrasts with the following well-known theorem of Kalton: If E is a separable symmetric sequence space such that the couple $$ \vec E $$ is -monotone, then either E = l p (1 ≤ p < ∞) or E = c 0.
Starting Page	212
Ending Page	215
Page Count	4
File Format	PDF
ISSN	00162663
Journal	Functional Analysis and Its Applications
Volume Number	44
Issue Number	3
e-ISSN	15738485
Language	English
Publisher	Springer US
Publisher Date	2010-09-22
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	interpolation of operators Peetre -functional -monotone Banach couple shift-invariant space Functional Analysis Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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On stably -monotone Banach couples