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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 3, Pages 60–63 (Mi faa205)  

Brief communications

On the Exact $\mathcal{K}$-Monotonicity of Banach Couples

S. V. Astashkin

Samara State University

Abstract: We present necessary and sufficient conditions for a Banach couple formed by the space $L_{\infty}$ and an arbitrary Lorentz space $\Lambda(\varphi)$ to be exact $\mathcal{K}$-monotone. The proof relies on the description of the set of extreme points of a $\mathcal{K}$-orbit for appropriate finite-dimensional couples. As a consequence of this description, we obtain a generalization of a well-known Markus theorem.

Keywords: Peetre $\mathcal{K}$-functional, exact $\mathcal{K}$-monotone Banach couple, Lorentz space, rearrangement, extreme point, convex hull

DOI: https://doi.org/10.4213/faa205

Full text: PDF file (144 kB)
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English version:
Functional Analysis and Its Applications, 2002, 36:3, 217–219

Bibliographic databases:

UDC: 517.982.27
Received: 19.03.2001

Citation: S. V. Astashkin, “On the Exact $\mathcal{K}$-Monotonicity of Banach Couples”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 60–63; Funct. Anal. Appl., 36:3 (2002), 217–219

Citation in format AMSBIB
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\pages 60--63
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