In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C∗-algebra A any densely defined A-linear clo...

In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined closed operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined closed operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C*-algebra A any densely define...

We will show that Feichtinger’s algebra S0(R ) (also known as modulation space M 0 (R ) and well defined for general locally compact Abelian groups) is a natural Hilbert module for quantum tori and that a result by V. Losert can be interpreted as implying that the construction of such Hilbert modules gives Feichtinger’s algebra, if one considers the category of time-frequency invariant homogeno...

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

We introduce a combinatorial way of calculating the Hilbert series of bigraded Sn-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald formula for HallLittlewood polynomial and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we give the way of associating the fillings giving the monomial term...

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related linear operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that admit an orthonormal modular Riesz basis. Interrelations and applications t...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be again...

We review some of our results from the theory of product systems of Hilbert modules [BS00, BBLS00, Ske00a, Ske01, Ske02, Ske03]. We explain that the product systems obtained from a CP-semigroup in [BS00] and in [MS02] are commutants of each other. Then we use this new commutant technique to construct product systems from E0–semigroups on Ba(E) where E is a strongly full von Neumann module. (Thi...

A notion of curvature is introduced in multivariable operator theory. The curvature invariant of a Hilbert module over C[z(1),., z(d)] is a nonnegative real number which has significant extremal properties, which tends to be an integer, and which is hard to compute directly. It is shown that for graded Hilbert modules, the curvature agrees with the Euler characteristic of a certain finitely gen...