Let M be a finite module and let I be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of I on M using the 0th local cohomology functor. We show that our definition re-conciliates with that of Ciupercă. By generalizing Singh’s formula (which holds in the case of λ(M/IM)<∞), we prove that the generalized Hilbert coefficients j0, . . . , jd−2 are preserv...

Let T be an adjointable operator on a Hilbert $$C^*$$ -module such that has the polar decomposition $$T=U\vert T\vert $$ . For each natural number n, is called $$(n+1)$$ -centered if $$T^k=U^k\vert T^k\vert for $$1\le k\le n+1$$ This paper initiates study of via generalized Aluthge transform and iterative transform. Some new characterizations are provided.

We study a natural Hodge module on the Hilbert scheme of four points on affine three-space, which categorifies the Donaldson–Thomas invariant of the Hilbert scheme. We determine the weight filtration on the Hodge module explicitly in terms of intersection cohomology complexes, and compute the E-polynomial of its cohomology. The computations make essential use of a description of the singularity...

For W*-algebras A and self-dual Hilbert A-modules M we show that every selfadjoint, ”compact” module operator on M is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.

We show that every Hilbert C∗-module E is a JB∗-triple in a canonical way and establish an explicit expression for the holomorphic automorphisms of the unit ball of E. 1.

In the present paper, we give a short proof of the nuclearity property of a class of CuntzPimsner algebras associated with a HilbertA-bimodule M, whereA is a separable and nuclear C*-algebra. We assume that the left A-action on the bimodule M is given in terms of compact module operators and that M is direct summand of the standard Hilbert module over A.

1 Veronese rings, Segre embeddings or more generally Segre-Veronese embeddings are very important rings in Algebraic Geometry. In this paper we present an original, elementary way to compute the Hilbert-Poincare series of these rings, as a consequence we compute their Castelnuovo-Mumford regularity, and also the leading term of the h−vector. Moreover, we can compute the Castelnuovo-Mumford regu...

We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a Hilbert C∗-module. We give an axiomatic description and discuss some applications. One of them is the definition a noncommutative Maslov index for paths of Lagrangians which appears in a splitting formula for the spectral flow. Analogously we study the spectral flow for odd operators on...