LetH be a Hilbert space, L(H) the algebra of all bounded linear operators onH and 〈, 〉A : H ×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉 , ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = QA} for different choices...

Using the Bloch representation of anN -dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.

Non-commutative multi-variable versions of weighted shifts arise naturally as ‘weighted’ left creation operators acting on Fock space. We investigate the unital wot-closed algebras they generate. The unweighted case yields non-commutative analytic Toeplitz algebras. The commutant can be described in terms of weighted right creation operators when the weights satisfy a condition specific to the ...

Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials Tuncay Aktosun,1,a) Paul Sacks,2,b) and Mehmet Unlu3,c) 1Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408, USA 2Department of Mathematics, Iowa State University, Ames, Iowa 24061, USA 3Department of Mathematics, Recep Tayyip Erdogan University, 5310...

We consider C = A+B where A is selfadjoint with a gap (a, b) in its spectrum and B is (relatively) compact. We prove a general result allowing B of indefinite sign and apply it to obtain a (δV ) bound for perturbations of suitable periodic Schrödinger operators and a (not quite) Lieb–Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices.

We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint n× n matrices.

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...