Related papers: Reverse triangle inequality in Hilbert $C^*$-modul…

We introduce the notion of finite right (respectively left) numerical index on a bimodule $X$ over C*-algebras A and B with a bi-Hilbertian structure. This notion is based on a Pimsner-Popa type inequality. The right (respectively left)…

We prove that the $L_1$-norms associated with a positive element $a$ of a unital C*-algebra are equivalent to the norm of C*-algebra if and only if $a$ is invertible.

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…

In this article, we study tensor product of Hilbert $C^*$-modules and Hilbert spaces. We show that if $E$ is a Hilbert $A$-module and $F$ is a Hilbert $B$-module, then tensor product of frames (orthonormal bases) for $E$ and $F$ produce…

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of…

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

We show by (counter)example that the intersection of complemented submodules in a Hilbert $C^*$-module is not necessarily complemented, answering an open question from [MR].

We show that if $(X.A)$ and $(Y,B)$ are two isomorphic Hilbert pro-$C^{\ast} $-bimodules, then the crossed product $A\times_{X}\mathbb{Z}$ of $A$ by $X$ and the crossed product $B\times_{Y}\mathbb{Z}$ of $B$ by $Y$ are isomorphic as…

Let $A$ be a $m\times m$ complex matrix with zero trace. Then there are $m\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and $\|B\|\|C\|_2\le (\log m+O(1))^{1/2}\|A\|_2$ where $\|D\|$ is the norm of $D$ as an operator on $\ell_2^m$ and…

We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of…

We introduce the notion of regularity for a relative holonomic $\mathcal D$-module in the sense of arXiv:1204.1331. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of…

We introduce the $B$-spline interpolation problem corresponding to a $C^*$-valued sesquilinear form on a Hilbert $C^*$-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when…

Khosravi, Drnov\v{s}ek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital…

We improve upon a result of Steinerberger (2024) by demonstrating that for any fixed $k \in \mathbb{N}$ and sufficiently large $n$, there exist integers $1 \leq a_1, \dots, a_k \leq n$ satisfying: \begin{align*} 0 < \left\| \sum_{j=1}^{k}…

We initiate a study of Hilbert modules over the polynomial algebra A=C[z_1,...,z_d] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity…

We present a generalization of Krein-\v{S}mul'jan theorem which involves several operators. Given bounded selfadjoint operators $A,B_1,\ldots,B_m$ acting on a Hilbert space $\mathcal{H}$, we provide sufficient conditions to determine…

Suppose $\mathcal{H}_1, \mathcal{H}_2, \ldots, \mathcal{H}_n$ are arbitrary complex Hilbert spaces, and ${\bf A}=[A_{ij}]$ is an $n\times n$ operator matrix with $A_{ij}\in \mathcal{B}(\mathcal{H}_j, \mathcal{H}_i).$ We show that $w({\bf…

In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse problem in the most general case where the self-adjoint,…

C*-endomorphisms arising from superselection structures with non-trivial centre define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the…

In this paper we view some fundamentals of the theory of Hilbert C*-modules and examine some ways in which Hilbert C*-modules differ from Hilbert spaces.