# G-Frames and Direct Sums

## Related Articles

- WEIGHTED HANKEL OPERATORS AND MATRICES. Datt, Gopal; Porwal, Deepak Kumar // Matematicki Vesnik;2013, Vol. 65 Issue 3, p353
In this paper, the notions of weighted Hankel matrix along with weighted Hankel operator S Î²Ï•, with Ï• âˆˆ Lâˆž(Î²) on the space LÂ²(Î²), Î² = {Î²n}nâˆˆZ being a sequence of positive numbers with Î²0 = 1, are introduced. It is proved that an operator on LÂ²(Î²)...

- EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE. DEEPA, K. P.; PANDIAN, S. CHENTHUR // International Journal of Engineering Science & Technology;May2012, Vol. 4 Issue 5, p2334
In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy...

- Simpler Proof of the Ringrose's Characterization of Compact Operators. Shukurov, Aydin Sh. // European Journal of Pure & Applied Mathematics;2015, Vol. 8 Issue 4, p499
The aim of this note is to give short, simpler and elementary proof of one characterization of compact operators via orthonormal sequences, which, hopefully will make this fact more accessible to nonspecialists and to a wide audience (especially to students). Beside this, the proof given here...

- Diagrammatic complete active space perturbation theory. Finley, James P. // Journal of Chemical Physics;1/15/1998, Vol. 108 Issue 3, p1081
Formulates a diagrammatic complete active space second-order perturbation theory. Basis of the theory formulation; Importance of wave operators in all Hilbert space methods; Limitation of the multireference perturbation theory; Computation of the final energy in the same manner as with state...

- The structure of an isometric tuple. Kennedy, Matthew // Proceedings of the London Mathematical Society;May2013, Vol. 106 Issue 5, p1157
An n-tuple of operators (V1, â€¦, Vn) acting on a Hilbert space H is said to be isometric if the operator [V1â‹¯Vn]:Hnâ†’H is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the classical Lebesgueâ€“von Neumannâ€“Wold...

- G-frames as Sums of Some g-orthonormal Bases. ABDOLLAHPOUR, MOHAMMAD REZA; NAJATI, ABBAS // Kyungpook Mathematical Journal;Mar2013, Vol. 53 Issue 1, p135
In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.

- A Theory of Summability on a Space of Generalized Functions. Khan, Khaula Naeem; Lamb, Wilson // Journal of Function Spaces & Applications;2013, p1
A theory of summability of orthonormal sets is introduced in multinormed spaces. The approach which is presented caters for infinite sets {Ã¸j}jÎµj, where the index set may be uncountable, and is applied to obtain convergence results in appropriate spaces of test functions and corresponding...

- Operator Characterizations and Some Properties of g-Frames on Hilbert Spaces. Xunxiang Guo // Journal of Function Spaces & Applications;2013, p1
Given the g-orthonormal basis for Hilbert space H, we characterize the g-frames, normalized tight g-frames, and g-Riesz bases in terms of the g-preframe operators. Then we consider the transformations of g-frames, normalized tight g-frames, and g-Riesz bases, which are induced by operators and...

- A short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some Fock-Bargmann space. Intissar, Abdelkader // Journal of Mathematical Physics;Jan2014, Vol. 55 Issue 1, p1
Let Æ’Î±(C) be the Hilbert space generated by the orthonormal basis enÎ±,v (z) = (2v/Î )1/4evzÂ²/2 e-Î Â²(n+Î±)Â²+2iÎ (n+Î±)z/v ; n âˆˆ N where v > 0 and Î± are real numbers, this space is a particular case of (Î¤, X)-theta Fock-Bargmann spaces recently constructed...