Operator Ideals and Operator Spaces
Copyright policy )Operator Ideals and Operator Spaces
We prove that every full symmetrically normed ideal of operators on a Hilbert space is realizable as the set of completely bounded maps between two homogeneous operator Hilbert spaces, with the c.b. norm equivalent to (but in general not equal to) the symmetric norm. We show that one can have equality of the c.b. norm and the symmetric norm if one leaves the category of operator spaces and passes to a slightly larger category.
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), c.b. norm, Interpolation between normed linear spaces, Norms (inequalities, more than one norm, etc.) of linear operators, Operator ideals, completely bounded maps between two homogeneous operator Hilbert spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), symmetric norm, category of operator spaces, Spaces of linear operators; topological tensor products; approximation properties, full symmetrically normed ideal of operators on a Hilbert space, Spaces of operators; tensor products; approximation properties
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), c.b. norm, Interpolation between normed linear spaces, Norms (inequalities, more than one norm, etc.) of linear operators, Operator ideals, completely bounded maps between two homogeneous operator Hilbert spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), symmetric norm, category of operator spaces, Spaces of linear operators; topological tensor products; approximation properties, full symmetrically normed ideal of operators on a Hilbert space, Spaces of operators; tensor products; approximation properties
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