Crossed products of Hilbert $C*$-modules

Products Of EP Operators On Hilbert C*-Modules

In this paper, the special attention is given to the  product of two  modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented  that imply  the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved  that $P(RPQ)$ is idempotent, if $RPQ$†</...

Inner Products and Module Maps of Hilbert C∗-modules

Let E and F be two Hilbert C∗-modules over C∗-algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and φ a map from A into B. We will prove in this paper that if the C∗-algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a ∗-isomorphism φ between the C∗-algebras such that 〈Tx, Ty〉 = φ(〈x, y〉), and T (xa) ...

Dynamical Systems on Hilbert C*-Modules

Frames and bases in tensor products of Hilbert spaces and Hilbert C∗-modules

Abstract. In this article, we study tensor product of Hilbert C∗-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A⊗B-module E ⊗F , and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H an...

Hilbert modules over pro-C*-algebras

In this paper, we generalize some results from Hilbert C*-modules to pro-C*-algebra case. We also give a new proof of the known result that l2(A) is aHilbert module over a pro-C*-algebra A.