Continuity of Functionals ..and Compact Action of Operators
نویسنده
چکیده
This thesis deals with two topics in Functional Analysis. The first three chapters are concerned with positive linear functionals on Banach *-algebras, whil^ the last two deal with operators that act compactly on an algebra of operators.
منابع مشابه
On genuine Lupac{s}-Beta operators and modulus of continuity
In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention results on the weighted modulus of continuity for the genuine operators.
متن کاملApproximation Theory and Functional Analysis on Time Scales
Here we start by proving the Riesz representation theorem for positive linear functionals on the space of continuous functions over a time scale. Then we prove further properties for the related Riemann–Stieltjes integral on time scales and we prove the related Hölder’s inequality. Next we prove the Hölder’s inequality for general positive linear functionals on time scales. We introduce basic c...
متن کاملShift 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 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