Article

Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions

Vladimir ChilinDepartment of Mathematics, Tashkent State University, Tashkent 700095, UzbekistanPeter G. DoddsDepartment of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, AustraliaA. A. SedaevFedor SukochevDepartment of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia

Transactions of the American Mathematical Societyjournal1996en

ABI

Abstract

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.

Topics

Advanced Banach Space Theory Advanced Harmonic Analysis Research Approximation Theory and Sequence Spaces

Identifiers

DOI: 10.1090/s0002-9947-96-01782-5

Citations and references

Cited by 2 14 references

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