In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

‎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...

‎In this paper we study the residual spectrum of the quasi-split unitary group $G=U(n,n)$ defined over a number field $F$‎, ‎coming from the Borel subgroups‎, ‎$L_{dis}^2(G(F)backslash G(Bbb A))_T$‎. ‎Due to lack of information on the local results‎, ‎that is‎, ‎the image of the local intertwining operators of the principal series‎, ‎our results are incomplete‎. ‎However‎, ‎we describe a conjec...

In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of ra...

in this paper we consider c0-group of unitary operators on a hilbert c*-module e. in particular we show that if a?l(e) be a c*-algebra including k(e) and ?t a c0-group of *-automorphisms on a, such that there is x?e with =1 and ?t (?x,x) = ?x,x t?r, then there is a c0-group ut of unitaries in l(e) such that ?t(a) = ut a ut*.

A theory of non-unitary unbounded similarity transformation operators is developed. To this end the class of J-unitary operators U is introduced. These operators are similar to unitary operators in their algebraic aspects but differ in their topological properties. It is shown how J-unitary operators are related to so-called J-biorthonormal systems and J-selfadjoint projections. Families {Uα} o...

Dedicated to Professor Shmuel Friedland. Abstract Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A1, . . . , Ak ∈ B(H) such that for any unitary operators U1, . . . , Uk, ∑k j=1 U ∗ j AjUj is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators. ...