A Note On Compact Operators Via Orthogonality

A Note on Compact Markov Operators

Let (X,P ) be an irreducible, random walk on the state space X which is at most countable. We suppose that the (usually infinite) stochastic matrix P describes a Markov chain {Zn}n∈N defined on a probability space (Ω,F ,P) with transition probabilities p(x, y) := P[Zn+1 = y|Zn = x] homogeneous in time. Besides we consider the n-step transition probabilities {p(x, y)}x,y∈X which represent the st...

A characterization of orthogonality preserving operators

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

A note on orthogonality and stable embeddedness

Orthogonality between two stably embedded definable sets is preserved under the addition of constants.

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.

A Note on Weighted Composition Operators on L^p-Spaces