Related papers: Split Clifford modules over a Hilbert space

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…

Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in…

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that…

An algebraic description of basic discrete symmetries (space reversal P, time reversal T and their combination PT) is studied. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers…

In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.

In this work, a connection between some spectral properties of direct integral of operators in the direct integral of Hilbert spaces and their coordinate operators has been investigated.

A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is…

In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over…

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the…

We look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting $d$-tuples of Hermitian elements of a $C^*$-algebra. The emphasis is on theoretical calculations of examples, in particular for…

This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex operator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex operator algebra over any field F of finite characteristic different from 2. We…

We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…

We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.

In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in…