Generalized atomic subspaces for operators in Hilbert spaces

$G$-Frames for operators in Hilbert spaces

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

Generalized Frames in Hilbert Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Multipliers of generalized frames in Hilbert spaces

Inequalities for Normal Operators in Hilbert Spaces

Let (H ; 〈·, ·〉) be a complex Hilbert space and T : H → H a bounded linear operator on H. Recall that T is a normal operator if T T = TT . Normal operators may be regarded as a generalisation of self-adjoint operator T in which T ∗ need not be exactly T but commutes with T [11, p. 15]. The numerical range of an operator T is the subset of the complex numbers C given by [11, p. 1]: W (T ) = {〈Tx...