A note on compact normal operators

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 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

A Note on Compact Semirings

By a topological semiring we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that x(y-{-z)=xy-\-xz and (x-\-y)z = xz-\-yz for all x, y, and z in 5. Note that, in contrast to the purely algebraic situation, we do not postulate the existence of an additive ide...

A note on $lambda$-Aluthge transforms of operators

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...