On operators preserving a conjugate space

A characterization of orthogonality preserving operators

‎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...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

A new sequence space and norm of certain matrix operators on this space

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of fin...

Time- Frequency Distributions Based on Conjugate Operators*

New classes of quadratic time-frequency representations (QTFRs), such as the affine, hyperbolic, and power classes, are interesting alternatives to the conventional shift-covariant class (Cohen's class). This paper studies new QTFR classes that retain the inner structure of Cohen's class. These classes are based on a pair of "conjugate" unitary operators and satisfy covariance and marginal prop...

On the Rate of Convergence of the Conjugate Gradient Method for Linear Operators in Hilbert Space