In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in gener...In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.展开更多
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated wit...In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual g-basis are continuous. Finally we consider the stability of g-bases under small perturbations. We generalize two results of Krein- Milman-Rutman and Paley-Wiener [7] to the situation of g-basis.展开更多
In this paper we develop the orthogonal projections and e-projections in Banach algebras. We prove some necessary and sufficient conditions for them and their spectrums. We also show that the sum of two generalized or...In this paper we develop the orthogonal projections and e-projections in Banach algebras. We prove some necessary and sufficient conditions for them and their spectrums. We also show that the sum of two generalized orthogonal projections u and v is a generalized orthogonal projection if, uv=vu=0. Our results generalize the results obtained for bounded linear operators on Hilbert spaces.展开更多
文摘In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
文摘In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual g-basis are continuous. Finally we consider the stability of g-bases under small perturbations. We generalize two results of Krein- Milman-Rutman and Paley-Wiener [7] to the situation of g-basis.
文摘In this paper we develop the orthogonal projections and e-projections in Banach algebras. We prove some necessary and sufficient conditions for them and their spectrums. We also show that the sum of two generalized orthogonal projections u and v is a generalized orthogonal projection if, uv=vu=0. Our results generalize the results obtained for bounded linear operators on Hilbert spaces.
