in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

the main purpose of this paper is to detemine the fine spectrum of the generalized difference operator delta_{uv} over the sequence space c0. these results are more general than the fine spectrum of the generalized difference operator delta_{uv} of srivastava and kumar.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh's theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.