CLASS OF (A,n)-POWER QUASI-NORMAL OPERATORS IN SEMI-HILBERTIAN SPACES

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

A 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.

Quasi-compact Operators in Topological Linear Spaces

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

On the Spectra of Semi-normal Operators

On the Structure of Semi-normal Operators

1. Preliminaries. Only bounded operators on a Hilbert space § of elements x will be considered. If A is self-ad joint with the spectral resolution (1) A=f\dE(k), and if ^a = £>aC4) denotes the set of elements x for which ||E(X)#|| is an absolutely continuous function of X, then § 0 is a subspace; cf. [2, p. 240], [3, p. 436] and [6, p. 104]. If £ = £«, then A is called absolutely continuous. Th...