- Sided M - Ideals and Multipliers in Operator Spaces
نویسندگان
چکیده
The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is an operator A–B-bimodule for C *-algebras A and B, then the module operations on X are automatically weak * continuous. One sided L-projections are introduced, and analogues of various results from the classical theory are proved. An assortment of examples is considered.
منابع مشابه
One - Sided M - Ideals and Multipliers in Operator Spaces , I
The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...
متن کاملOperator Spaces Which Are One-sided M-ideals in Their Bidual
We generalize an important class of Banach spaces, namely the M embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M -embedded operator spaces are the operator spaces which are one-sided M -ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension proper...
متن کاملMultiplier operator algebras and applications.
The one-sided multipliers of an operator space X are a key to "latent operator algebraic structure" in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals.
متن کاملMultipliers of continuous $G$-frames in Hilbert spaces
In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.
متن کاملSome algebraic properties of Lambert Multipliers on $L^2$ spaces
In this paper, we determine the structure of the space of multipliers of the range of a composition operator $C_varphi$ that induces by the conditional expectation between two $L^p(Sigma)$ spaces.
متن کامل