Derivations of τ-measurable Operators

Weigt, Martin

doi:10.1007/978-3-0346-0174-0_14

Cited by 7 publications

(6 citation statements)

References 19 publications

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“…Moreover, very little is known about unbounded *-derivations and tensor products in the framework of unbounded operator algebras. The reader is referred to as [15,16,18,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

Representable and Continuous Functionals on Banach Quasi *-Algebras

Adamo

Trapani

2017

Mediterr. J. Math.

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In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.

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“…Moreover, very little is known about unbounded *-derivations and tensor products in the framework of unbounded operator algebras. The reader is referred to as [15,16,18,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

Representable and Continuous Functionals on Banach Quasi *-Algebras

Adamo

Trapani

2017

Mediterr. J. Math.

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“…This means that in the case of Z being atomic, every derivation on LS(M ) is automatically Z-linear. Combining this fact with Theorem 3.5, we have the following result which is a strengthening of result obtained by Weigt in [58]. Now let us consider derivations on the algebra S 0 (M, τ ) of τ -compact operators affiliated with a semi-finite von Neumann algebra M and a faithful normal semifinite trace τ (see [3], [6]).…”

Section: Now We Shall Consider Derivations On Algebras Of Locally Meamentioning

confidence: 53%

Derivations, local and 2-local derivations on algebras of measurable operators

Ayupov¹,

Kudaybergenov²

2016

Topics in Functional Analysis And Algebra

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The present paper presents a survey of some recent results devoted to derivations, local derivations and 2-local derivations on various algebras of measurable operators affiliated with von Neumann algebras. We give a complete description of derivation on these algebras, except the case where the von Neumann algebra is of type II 1 . In the latter case the result is obtained under an extra condition of measure continuity of derivations. Local and 2local derivations on the above algebras are also considered. We give sufficient conditions on a von Neumann algebra M , under which every local or 2-local derivation on the algebra of measurable operators affiliated with M is automatically becomes a derivation. We also give examples of commutative algebras of measurable operators admitting local and 2-local derivations which are not derivations.

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“…[2, 8, 9, 10, 24, 25, 29, 38, 39]). Application of the Ryll-Nardzewski fixed point theorem to derivation problems is suggested in [26] (see also [8], [24] and [47]). In general, Ryll-Nardzewski fixed point theorem is not applicable when the symmetric space is L 1 (M, τ ) as it is not reflexive and therefore the unit ball of it is not weakly compact.…”

Section: Applications To Derivation Problemmentioning

confidence: 99%

M-embedded symmetric operator spaces and the derivation problem

Huang¹,

Levitina²,

Sukochev³

2019

Math. Proc. Camb. Phil. Soc.

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Let ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is not a superset of the set of all bounded vanishing functions on (0, ∞). In this paper, we prove that the corresponding operator space E(ℳ, τ) is also M-embedded. It extends earlier results by Werner [48, Proposition 4∙1] from the particular case of symmetric ideals of bounded operators on a separable Hilbert space to the case of symmetric spaces (consisting of possibly unbounded operators) on an arbitrary semifinite von Neumann algebra. Several applications are given, e.g., the derivation problem for noncommutative Lorentz spaces ℒp,1(ℳ, τ), 1 < p < ∞, has a positive answer.

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Derivations of τ-measurable Operators

Cited by 7 publications

References 19 publications

Representable and Continuous Functionals on Banach Quasi *-Algebras

Representable and Continuous Functionals on Banach Quasi *-Algebras

Derivations, local and 2-local derivations on algebras of measurable operators

M-embedded symmetric operator spaces and the derivation problem

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