Search

In a quantum system, equilibrium points are usually defined by the equation of evolution. The analysis of this process is often done by Schrödinger equation, and by linear operators on a Hilbert space. Regardless of the fact that calculations are based on static-point metrics, due to the chaotic behavior, the realization of practical conditions on space and mappings will be relatively difficult. In addition, access to constructive arguments will enable us to provide a computational method. In this paper, at first we define a probabilistic measurement and combine it with probabilistic domains to obtain a probabilistic model suitable for quantum systems. By extending the mappings to nonlinear operators, we examine the conditions under which stable equilibrium points can be reached. In the application section, using the evolution equation, we will determine the stationary points based on their spectral properties. Also there will be possible to generalize this method to simultaneous measurements. [ABSTRACT FROM AUTHOR]

In this paper, we consider some kinds of semiregular frames of translates on the Hilbert space L 2 (R d ). More precisely, we investigate the frames of the form {TAkf}k∈Zd where A is a real invertible d × d matrix, f ∈ L 2 (R d ) and it is a frame for the closed subspace generated by {TAkf}k∈Zd. [ABSTRACT FROM AUTHOR]

Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled fusion frames on Hilbert spaces. It is shown that controlled fusion frames are a generalization of fusion frames giving a generalized way to obtain numerical advantage in the sense of preconditioning to check the fusion frame condition. For this end, we introduce the notion of Q-duality for Controlled fusion frames. Also, we survey the robustness of controlled fusion frames under some perturbations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce an equivalence relation on the space of real valued statistically convergence sequences, Cst, and an inner product on the set of its equivalence classes. We equip Cst with the induced J-metric, dJ, by the given inner product. We prove that Cst is a complete J-metric space. We also show that the space of all real valued convergent sequences is a dense subspace of (Cst; dJ). [ABSTRACT FROM AUTHOR]

This paper was aimed at studying some novel methods of constructing new c-K-g-frames in a Hilbert space H. Some necessary and sufficient conditions were given for some bounded operators on H under which new c-K-g-frames were obtained from the existing ones. Also, the sum of c-K-g-frames were discussed, some of their characteri- zations were identified, and some bounded operators offered to construct new c-K-g-frames from the old ones. [ABSTRACT FROM AUTHOR]

This paper was aimed at studying some novel methods of constructing new c-K-g-frames in a Hilbert space H. Some necessary and sufficient conditions were given for some bounded operators on H under which new c-K-g-frames were obtained from the existing ones. Also, the sum of c-K-g-frames were discussed, some of their characteri-zations were identified, and some bounded operators offered to construct new c-K-g-frames from the old ones. [ABSTRACT FROM AUTHOR]

Suppose that T is a bounded operator from a Hilbert space H into H. In this paper, for an injective cohyponormal or complex symmetric operator T, we find a necessary and sufficient condition for T to have the Hyers-Ulam stability. Moreover, when T is injective, we find necessary and sufficient conditions for T∗T to have the Hyers-Ulam stability [ABSTRACT FROM AUTHOR]

Let σ be a linear *-endomorphism on a C* -algebra A so that σ(A) acts on a Hilbert space H which including K(H) and let {α}teR be a σ-C*-dynamical system on A with the generator δ: In this paper, we demonstrate some conditions under which ftgt2R is implemented by a C0-groups of unitaries on H. In particular, we prove that for a rank- one projection p 2 A; which is invariant under t; there is a C0-group futgt2R of unitaries in B(H) such that t(a) = utσ(a)u t: Furthermore, introducing the concepts of σ-inner endomorphism and σ-bijective map, we prove that each σ-bijective linear endomorphism on A is a σ-inner endomorphism, where σ ia idempotent. Finally, as an application, we characterize each so-called σ-C -dynamical system on the concrete C - algebra A:= B(H) B(H); where H is a separable Hilbert space and σ is the linear-endomorphism σ(S; T) = (0; T) on A:. [ABSTRACT FROM AUTHOR]

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A;B 2 B(H), define the bimultiplication operator M2;A;B on the class of Hilbert-Schmidt operators by M2;A;B(X) = AXB. In this paper, we show that if B, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) W0(M2;A;B); where co stands for the convex hull and W0(:) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2;A;B): [ABSTRACT FROM AUTHOR]

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A;B 2 B(H), define the bimultiplication operator M2;A;B on the class of Hilbert-Schmidt operators by M2;A;B(X) = AXB. In this paper, we show that if B, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) W0(M2;A;B); where co stands for the convex hull and W0(:) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2;A;B): [ABSTRACT FROM AUTHOR]

In this paper, we study coposinormal composition operators and posinormal weighted composition operators on the Hardy space H²(D). We show that if Wψ,φ is coposinormal on H²(D), then ψ never vanishes on D also we prove that φ is univalent. Moreover, we study the commutant of a coposinormal weighted composition operator. [ABSTRACT FROM AUTHOR]

In this article, first we are going to review the concept of ordinary frames, in more general case in measure spaces, namely, gcframes. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa. [ABSTRACT FROM AUTHOR]