Frames and generalized operator orbits

Operator-valued Frames

We develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

Similar generalized frames

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

Generalized Frames in Hilbert Spaces

Orbits of operators and operator semigroups

Denote byB(X) the set of all bounded linear operators acting on a Banach spaceX . For simplicity we assume that all Banach spaces are complex unless stated explicitly otherwise. However, the notions make sense also in real Banach spaces and most of the results remain true (with slight modifications) in the real case. Let X be a Banach space and let T be a bounded linear operator on X . By an or...

OPERATOR PARAMETERIZATIONS OF g-FRAMES

Abstract. In this paper, we mainly parameterize g-frames in Hilbert space in terms of operators. Firstly, under the condition that there exists a g-orthonormal basis we establish the one to one correspondence between different kinds of g-frames with certain kinds of operators. Then we parameterize g-frames without the above restriction. Finally, we consider some special g-frames, and their oper...