1995
DOI: 10.1007/bf01378783
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Topological and bornological characterisations of ideals in von Neumann algebras: I

Abstract: Suppose .M is a von Neumann algebra on a Hilbert space 7-( and 2-is any ideal in 34. We determine a topology t(Z) on 7-/, for which the members of M that are t(g) to norm continuous are exactly those in 2"; and a bornology b(2.) on 7-/such that the elements of M which map the unit ball to an element of b(2.), equivalently those members of 34 that are norm to b(2.) bounded, are exactly those in 2". This is achieved via analogues of the notions of injeetivity and surjectivity in the theory of operator ideals on … Show more

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Cited by 4 publications
(6 citation statements)
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“…With respect to this pairing, a subset of 7-( is t(I)-equicontinuous if and only it belongs to b(I). Proofs and more information can again be found in [12].…”
Section: The Topology T(i P)mentioning
confidence: 98%
See 2 more Smart Citations
“…With respect to this pairing, a subset of 7-( is t(I)-equicontinuous if and only it belongs to b(I). Proofs and more information can again be found in [12].…”
Section: The Topology T(i P)mentioning
confidence: 98%
“…The bornology b (2-v) determines the ideal ((2-v)), in the sense that b(2-p) = b(((2-P))). For proofs and additional information we refer the reader to [12].…”
Section: Bornological Characterisations Of Closed Idealsmentioning
confidence: 99%
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“…The explicit construction (with all arrows shown in the diagram) of the (upper) triangle is given in [32], in which several applications to Banach space theory are demonstrated. When the underlying space is a fixed complex Hilbert space, West implements the triangle in the context of operator algebras [25] and provides several applications with Conradie [1] (see Section 2). In this paper, we shall complete the LCS version of the triangle.…”
Section: Hogbe-nlendmentioning
confidence: 99%
“…In [16], we use these concepts in classifying locally convex spaces. They are also used by other authors in operator algebra theory in [13,2].…”
Section: Introductionmentioning
confidence: 99%