Unconditional bases in tensor products of Hilbert spaces
Copyright policy )Unconditional bases in tensor products of Hilbert spaces
We prove that a tensor norm $\alpha$ (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if $\ell_2\otimes\cdots\otimes \ell_2$, endowed with the norm $\alpha$, has an unconditional basis. This extends a classical result of Kwapień and Pełczyński. The symmetric version of that statement follows, and this extends a recent result of Defant, Díaz, García and Maestre.
Tensor products, Unconditional basis, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Hilbert-Schmidt norm, tensor products, Polynomials, 517.98, unconditional basis, (Spaces of) multilinear mappings, polynomials, Banach-spaces, Multilinear operators, Forms, Hilbert-Schmidt operators, Spaces of operators; tensor products; approximation properties, P-summing operators, Análisis funcional y teoría de operadores
Tensor products, Unconditional basis, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Hilbert-Schmidt norm, tensor products, Polynomials, 517.98, unconditional basis, (Spaces of) multilinear mappings, polynomials, Banach-spaces, Multilinear operators, Forms, Hilbert-Schmidt operators, Spaces of operators; tensor products; approximation properties, P-summing operators, Análisis funcional y teoría de operadores
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!