Related papers: Covariant version of the Stinespring type theorem …

A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

We introduce a Hilbert $A$-module structure on the higher oscillatory module, where $A$ denotes the $C^*$-algebra of bounded endomorphisms of the basic oscillatory module. We also define the notion of an exterior covariant derivative in an…

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

We introduce $C^*$-pseudo-multiplicative unitaries and (concrete) Hopf $C^*$-bimodules, which are $C^*$-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock,…

In this paper we show that under certain condition the Fontaine--Mazur $L$-invariant for a Hilbert eigenform coincides with its Teitelbaum type $L$-invariant, and thus prove a conjecture of Chida, Mok and Park.

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.

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.

We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.

A $C^*$-textile dynamical system $({\cal A}, \rho,\eta,\Sigma^\rho,\Sigma^\eta, \kappa)$ connsists of a unital $C^*$-algebra ${\cal A}$, two families of endomorphisms ${\rho_\alpha}_{\alpha \in \Sigma^\rho}$ and ${\eta_a}_{a \in…

We derive Paschke's GNS construction for completely positive maps on unital pro-C*-algebras from the KSGNS construction, presented by M. Joita [J. London Math. Soc. {\bf 66} (2002), 421--432], and then we deduce an analogue of Stinespring…

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…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

We generalize the work of Ohta on the congruence modules attached to elliptic Eisenstein series to the setting of Hilbert modular forms. Our work involves three parts. In the first part, we construct Eisenstein series adelically and compute…

Given a representation of a unital $C^*$-algebra $\mathcal{A}$ on a Hilbert space $\mathcal{H}$, together with a bounded linear map $V:\mathcal{K}\to\mathcal{H}$ from some other Hilbert space, one obtains a completely positive map on…

In this work, we initially compute the integral MW-motivic cohomology groups associated with Stiefel varieties. Then we proceed to establish the integral MW-motive decomposition of Stiefel varieties, which proves the conjecture in our…

In this paper, we define the notion of induced representations of a Hilbert $C^{*}$-module and we show that Morita equivalence of two Hilbert modules (in the sense of Moslehian and Joita), implies the equivalence of categories of…

We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with…

We use the homological perturbation lemma to give an explicit proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.