Vector-valued Invariant Means on Spaces of Bounded Operators Associated to a Locally Compact Group
نویسنده
چکیده
The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study vectorvalued means on S of π-(weakly) almost periodic operators on Hπ .
منابع مشابه
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کاملOperator Valued Series and Vector Valued Multiplier Spaces
Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous linear operators from $X$ into $Y$. If ${T_{j}}$ is a sequence in $L(X,Y)$, the (bounded) multiplier space for the series $sum T_{j}$ is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...
متن کاملWeighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملA Class of compact operators on homogeneous spaces
Let $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and $H$ be a compact subgroup of $G$. For an admissible wavelet $zeta$ for $varpi$ and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded compact operators which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.
متن کامل