C-symmetric operators and reflexivity

On a functional equation for symmetric linear operators on $C^{*}$ algebras

‎Let $A$ be a $C^{*}$ algebra‎, ‎$T‎: ‎Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $‎. ‎We prove that under each of the following conditions‎, ‎$T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: ‎‎ ‎i) $A$ is a simple $C^{*}$-algebra‎. ‎ii) $A$ is unital with trivial center and has a faithful trace such ...

Toeplitz Operators and Solvable C*-algebras on Hermitian Symmetric Spaces

Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...

On Reflexivity and Hyperreflexivity of Some Spaces of Intertwining Operators

Let T, T ′ be weak contractions (in the sense of Sz.-Nagy and Foiaş), m, m the minimal functions of their C0 parts and let d be the greatest common inner divisor of m, m . It is proved that the space I(T, T ) of all operators intertwining T, T ′ is reflexive if and only if the model operator S(d) is reflexive. Here S(d) means the compression of the unilateral shift onto the space H⊖dH. In parti...

Review: A C*-algebra approach to complex symmetric operators

Complex Symmetric Operators and Applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, selfadjoint extensions of s...