On $E$-frames in Hilbert spaces
H. Hedayatirad, T. L. Shateri
本文研究希尔伯特空间中的E-框架，提出受控E-框架概念，并完整刻画了给定受控E-框架的所有受控E-对偶。
本文阐述了关于这一概念的一些结果。此外，我们引入了受控E-框架的概念，并刻画了与给定受控E-框架相关联的所有受控E-对偶。
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
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A weak Hilbert space that is a twisted HIlbert space
构造了一个兼具弱希尔伯特与扭曲希尔伯特性质的空间，证明了此类空间的存在性。
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Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames in Hilbert $C^{\ast}$-Modules under perturbation and we establish some properties
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Generalized fusion frame in Quaternionic Hilbert spaces
本文研究四元数 Hilbert 空间中的广义融合框架，给出其基于框架算子的刻画，并利用可逆有界右 Q-线性算子构造 g-fusion frame。
Introduction of frame in tensor product of n-Hilbert spaces
本研究针对n-希尔伯特空间张量积仍为n-希尔伯特空间的特性，引入框架概念，推广基的相关结果，探究框架与有界线性算子的关系，并讨论对偶框架，拓展了n-希尔伯特空间框架理论的研究范畴。
In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
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Continuous frames in n-Hilbert spaces and their tensor products
该研究提出n-希尔伯特空间中连续框架的概念，将其推广至n-希尔伯特空间的张量积场景，并进一步研究了对应空间及张量积下的对偶连续框架与连续Bessel乘子。
In this paper, we introduce and we study the concept of Continuous Controlled K-Frame for Hilbert $C^{\ast}$-Modules wich are generalizations of discrete Controlled K-Frames.
We prove that any tight frame in Hilbert space can be obtained by the Kaczmarz algorithm. An explicit way of constructing this correspondence is given. The uniqueness of the correspondence is determined.
In this article, we introduce and study Riesz bases in a separable quaternionic Hilbert spaces. Some results on Riesz bases in a separable quaternionic Hilbert spaces are proved. It is also proved that a Riesz basis in a separable quaternionic Hilbert space a frame for the quaternionic Hilbert space. Riesz sequences are defined and equivalence of a Riesz basis and a complete Riesz sequence in a separable quaternionic Hilbert space is proved.
Hadamard's lemma in separable Hilbert spaces
该研究将阿达马引理推广至可分希尔伯特空间的框架下，实现了该引理在泛函分析领域更广泛空间中的应用。
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Constructions of bi-g-fusion frame in Hilbert space
该研究提出了希尔伯特空间中作为受控g-fusion框架推广的bi-g-fusion框架概念，给出示例并探讨了其在希尔伯特空间张量积中的情况。
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of frames in Hilbert spaces. In this papers we study the notion of dual continuous $K$-frames in Hilbert spaces. Also we etablish some new properties.
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The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded linear operator in tensor product of n-Hilbert spaces. At the end, the direct sum of controlled frames in n-Hilbert space is being considered.
Approximate isometries of Hilbert spaces
通过移除满射性假设，改进了实Hilbert空间等距映射的Hyers-Ulam稳定性结果。
We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.
We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of the space. We also construct a normalized frame for a Hilbert space which contains a subset which is a Schauder basis for H but does not contain any subset which is a Riesz basis for H.
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.
Nagy and Pollard-Hilding-Type Stability of Hilbert-Schmidt Frames
本文为可分Hilbert空间中Hilbert-Schmidt框架的扰动稳定性建立了基于Nagy型和Pollard-Hilding型不等式的充分条件，并提供了框架界的显式估计及示例。
We introduce the notion of continuous controlled g-fusion frame in Hilbert space which is the generalization of discrete controlled g-fusion frame and give an example. Some characterizations of continuous controlled g-fusion frame have been presented. We define the frame operator and multiplier of continuous controlled g-fusion Bessel families in Hilbert spaces. Continuous resolution of the identity operator on a Hilbert space using the theory of continuous controlled g-fusion frame is being considered. Finally, we discuss perturbation results of continuous controlled g-fusion frame.
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Concept of a family of local atoms in n-Hilbert space is being studied. K-frame in tensor product of n-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of n-Hilbert spaces is presented and established a relationship between atomic systems in n-Hilbert spaces and their tensor products.
We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted $\ell^2$ norms of the Dirichlet coefficients. We characterize the multiplier algebras for some of these spaces.
We use a technique of Szankowski to construct an operator Hilbert space that does not have the operator approximation property
Fusion frame and its alternative dual in tensor product of Hilbert spaces
该研究聚焦希尔伯特空间张量积中的融合框架，分析其相关性质与恒等算子的单位分解，并提出该场景下融合框架的替代对偶，丰富了泛函分析中融合框架的理论体系。
We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators on $\ell_p$ that are liftable / extensible through centralizers.
We prove that if a non-atomic separable Banach lattice in a weak Hilbert space, then it is lattice isomorphic to $L_2(0,1)$.
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In this paper we introduce and prove some properties of $(α;β)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of $(α,β)$-normal operators in semi Hilbertian spaces.
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On the Hilbert-type operators acting from function spaces into sequence spaces
本文研究从函数空间到序列空间的Hilbert型算子，给出其有界性与紧性的充要条件，并在特殊情形下得到范数的精确估计。
In this paper, we characterize and study the concept of controlled continuous $g$-frame which is an extension of continuous $g$-frame in Hilbert spaces. We introduce the concept of controlled continuous dual $g$-frame and observe some interesting properties of it. Finally, we characterize all controlled continuous dual $g$-frames of a controlled continuous $g$-frame.
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