Dijana Ilišević

On a class of projections on *-rings

ABSTRACT In this article we describe the structure of projections acting on semiprime *-rings and satisfying a certain functional identity. The main result is applied to bicircular projections on C *-algebras.

Perturbation of the Wigner equation in inner product C*-modules

Let A be a C*-algebra and B be a von Neumann algebra that both act on a Hilbert space H. Let M and N be inner product modules over A and B, respectively. Under certain assumptions, we show that for each mapping f:M→N satisfying ‖∣⟨f(x),f(y)⟩∣−∣⟨x,y⟩∣‖⩽φ(x,y) (x,y∊M), where φ is a control function, there exists a solution I:M→N of the Wigner equation ∣⟨I(x),I(y)⟩∣=∣⟨x,y⟩∣ (x,y∊M) such that ‖f(x)−I(x)‖⩽φ(x,x) (x∊M).

Gruss type inequalities in inner product modules

In this paper we give some properties of a generalized inner product in modules over H*-algebras and C*-algebras and we obtain inequalities of Griiss type.

Bessel and Grüss type inequalities in inner product modules

In this paper we give inequalities of Bessel type and inequalities of Gruss type in an inner product module over a proper H*-algebra or a C*-algebra.

On additivity of centralisers

Let R be a ring and let M be a bimodule over R . We consider the question of when a map φ: R → M such that φ( ab ) = φ (a)b for all a, b ∈ R is additive.

When is the Hermitian/skew-Hermitian part of a matrix a potent matrix?

This paper deals with the Hermitian H(A) and skew-Hermitian part S(A) of a complex matrix A. We characterize all complex matrices A such that H(A), respectively S(A), is a potent matrix. Two approaches are used: characterizations of idempotent and tripotent Hermitian matrices of the form � X Y � Y 0 � , and a singular value decomposition of A. In addition, a relation between the potency of H(A), respectively S(A), and the normality of A is also studied.

On square roots of isometries

Abstract In various normed spaces we answer the question of when a given isometry is a square of some isometry. In particular, we consider (real and complex) matrix spaces equipped with unitarily invariant norms and unitary congruence invariant norms, as well as some infinite dimensional spaces illustrating the difference between finite and infinite dimensions.

Generalized n-circular projections on JB*-triples and Hilbert C0(Ω)-modules

Abstract Being expected as a Banach space substitute of the orthogonal projections on Hilbert spaces, generalized n-circular projections also extend the notion of generalized bicontractive projections on JB*-triples. In this paper, we study some geometric properties of JB*-triples related to them. In particular, we provide some structure theorems of generalized n-circular projections on an often mentioned special case of JB*-triples, i.e., Hilbert C*-modules over abelian C*-algebras C0(Ω).

A quantitative version of Herstein’s theorem for Jordan -isomorphisms

We study linear mappings between -algebras and , which approximately satisfy Jordan multiplicativity condition and a -preserving condition (that is, the so-called -approximate Jordan -homomorphisms). We first prove that every such mapping is automatically continuous and we give the estimates of its norm, as well as the estimates of the norm of its inverse if it is bijective. If , , and is a bijective -approximate Jordan -homomorphism with sufficiently small , then either has a large norm, or is close to a Jordan -isomorphism, that is, to a mapping of the form , or , for some unitary . We also give the corresponding quantitative estimate.