In this paper, we study the concept of controlled ∗ -operator frames for space all adjointable operators on a Hilbert id="M4"> C -module H. Also, discuss characterizations id="M5"> and give some properties. Some illustrative examples are provided to advocate usability our results.

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concept frames for set all adjointable operators from ℋ to id="M2"> mathvariant="script">K their generalizations. Moreover, obtain some new results generalized Hilbert modules.

Suppose that $${\mathscr {E}}$$ and {F}}$$ are Hilbert $$C^*$$ -modules. We present a power-norm $$\left( \left\| \cdot \right\| ^{{\mathscr {E}}}_n:n\in {\mathbb {N}}\right) $$ based on obtain some of its fundamental properties. introduce new definition the absolutely (2, 2)-summing operators from to , denote set such by $${\tilde{\Pi }}_2({\mathscr {E}},{\mathscr {F}})$$ with convention {E}})...

The theory of product systems both of Hilbert spaces (Arveson systems) and product systems of Hilbert modules has reached a status where it seems appropriate to rest a moment and to have a look at what is known so far and what are open problems. However, the attempt to give an approximately complete account in view pages is destined to fail already for Arveson systems since Tsirelson, Powers an...

In this paper we study the unitary equivalence between Hilbert modules over a locally C∗-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C∗-algebra and show that a Hilbert module over a Fréchet locally C∗-algebra is countably generated if and only if the locally C∗-algebra of all ”compact” operators has an approximate unit. 2000 Mathemat...