Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.  

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

Let A be a complex unital Banach algebra with unit 1. The sets of all invertible and quasinilpotent elements (σ(a) = {0}) of A will be denoted by A and A, respectively. The group inverse of a ∈ A is the unique element a ∈ A which satisfies aaa = a, aaa = a, aa = aa. If the group inverse of a exists, a is group invertible. Denote by A the set of all group invertible elements of A. The generalize...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

In this paper, we clarify the applicability of the super operator technique for describing the dissipative quantum dynamics of a system consists of two qubits coupled with a thermal bath at finite temperature. By using super operator technique, we solve the master equation and find the matrix elements of the density operator. Considering the qubits to be initially prepared in a general mixed st...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...