Related papers: Bessel type inequalities in Hilbert C*-modules

Some sharp Bessel type inequalities for non-orthonormal families of vectors in inner product spaces are given. Applications for complex numbers are also provided.

In this paper, we study Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and related the harmonic function theory introduced by Muckenhoupt--Stein. We establish the Moser type inequality for these harmonic…

Continuous generalized fusion frame theory was recently introduced by Rahimi and al. Several equalities and inequalities have been obtained for frame, fusion generalized fusion frame, among others. In the present paper, we continue and…

We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.

For a unital $C^*$-algebra $\mathcal A$ and a subspace $\mathcal B$ of $\mathcal A$, a characterization for a best approximation to an element of $\mathcal A$ in $\mathcal B$ is obtained. As an application, a formula for the distance of an…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we…

We regard a right Hilbert C*-module X over a C*-algebra A endowed with an isometric *-homomorphism \phi: A\to L_A(X) as an object X_A of the C*-category of right Hilbert A-modules. Following a construction by the first author and Roberts,…

Bell inequalities for position measurements are derived using the bits of the binary expansion of position-measurement results. Violations of these inequalities are obtained from the output state of the Non-degenerate Optical Parametric…

In this paper, we will introduce the concept of biframes for Hilbert $ C^{\ast}- $modules produced by a pair of sequences, and we present various examples of biframes. Then, we examine the characteristics of biframes from the viewpoint of…

We introduce the concept of frame of multipliers in Hilbert modules over pro-C*-algebras and show that many properties of frames in Hilbert C*-modules are valid for frames of multipliers in Hilbert modules over pro-C*-algebras.

A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.

In the setting of the multidimensional Mellin analysis we introduce moduli of continuity and use them to define Besov-Mellin spaces. We prove that Besov-Mellin spaces are the interpolation spaces (in the sense of J.Peetre) between two…

We analyse the recent claim that a violation of a Bell's inequality has been observed in the $B$--meson system [A. Go, {\em Journal of Modern Optics} {\bf 51} (2004) 991]. The results of this experiment are a convincing proof of quantum…

The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or…

In this paper we establish Parseval type identities and surprising new inequalities for Hilbert-Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and G{\u{a}}vru{\c{t}}a.

Our main goal in this paper, is to generalize to Hilbert C*-modules the concept of fusion frames. Indeed we introduce the notion of *\~nfusion frames associated to weighted sequences of orthogonally complemented submodules of a Hilbert…

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.

We prove a covariant version of the Stinespring theorem for Hilbert C*-modules.

We show that elements of Hilbert $A$-module obtained by completion of the space of square-integrable functions on a space with measure $X$ taking values in a $C^*$-algebra $A$ cannot be viewed as $A$-valued functions on $X$ defined almost…