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Analytic semigroups on vector valued noncommutative $L^{p}$-spaces

100%

Arhancet C.

Studia Mathematica

2013

tom 216

nr 3

271-290

We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ($(T ⊗ Id_{E})_{t≥0}$ on the vector valued noncommutative $L^{p}$-space $L^{p}(M,E)$. Moreover, we give applications to the $H^{∞}(Σ_{θ})$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

Unconditionality, Fourier multipliers and Schur multipliers

100%

Arhancet C.

Colloquium Mathematicum

2012

tom 127

nr 1

17-37

Let G be an infinite locally compact abelian group and X be a Banach space. We show that if every bounded Fourier multiplier T on L²(G) has the property that $T ⊗ Id_X$ is bounded on L²(G,X) then X is isomorphic to a Hilbert space. Moreover, we prove that if 1 < p < ∞, p ≠ 2, then there exists a bounded Fourier multiplier on $L^{p}(G)$ which is not completely bounded. Finally, we examine unconditionality from the point of view of Schur multipliers. More precisely, we give several necessary and sufficient conditions for an operator space to be completely isomorphic to an operator Hilbert space.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Arhancet C.

1 2013

1 2012

Wyniki wyszukiwania

Analytic semigroups on vector valued noncommutative $L^{p}$-spaces

Unconditionality, Fourier multipliers and Schur multipliers