Duality and Lorentz-Marcinkiewicz operator spaces.
Copyright policy )Duality and Lorentz-Marcinkiewicz operator spaces.
Let \(S_{\phi,q}\) be the collection of all compact operators T on a (complex) Hilbert space H such that (INVALID INPUT)\(\sigma_{\phi,q}(T)=(\sum^{\infty}_{n=1}(\phi (n)s_ n(T))^{q_ n-1})^{1/q}0}(\phi (ts)/\phi (s))0\). The special case \(\phi (t)=t^{1/p}\) gives the operator space \((S_{p,q},\sigma_{p,q})\) introduced in 1967 by \textit{H. Triebel} [Invent. Math. 4, 275-279 (1967; Zbl 0165.145)]. We characterize the dual of \(S_{\phi,q}\). In particular, we prove that \((S_{p,q})'={\mathcal L}(H)\) for \(0
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Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), 510.mathematics, interpolation spaces, Abstract operator algebras on Hilbert spaces, dual, spaces of operators, Abstract interpolation of topological vector spaces, singular numbers, Article, compact operators
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), 510.mathematics, interpolation spaces, Abstract operator algebras on Hilbert spaces, dual, spaces of operators, Abstract interpolation of topological vector spaces, singular numbers, Article, compact operators
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