A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied for two coactions α, β : A → A⊗O, where A is the co...

The purpose of this paper is to throw a bridge between two seemingly unrelated subjects. One is the Hilbert scheme of points on projective surfaces, which has been intensively studied by various people (see e.g., [I, ES, Gö1, Gö2]). The other is the infinite dimensional Heisenberg algebra which is closely related to affine Lie algebras (see e.g., [K]). We shall construct a representation of the...

We present a hierarchy of covering properties of rational convex cones with respect to the unimodular subcones spanned by the Hilbert basis. For two of the concepts from the hierarchy we derive characterizations: a description of partitions that leads to a natural integer programming formulation for the Hilbert Partition problem, and a characterization of \binary covers" that admits a linear al...

It is well known that a function K : Ω × Ω → L(Y) (where L(Y) is the set of all bounded linear operators on a Hilbert space Y) being (1) a positive kernel in the sense of Aronszajn (i.e. ∑N i,j=1〈K(ωi, ωj)yj , yi〉 ≥ 0 for all ω1, . . . , ωN ∈ Ω, y1, . . . , yN ∈ Y, and N = 1, 2, . . . ) is equivalent to (2) K being the reproducing kernel for a reproducing kernel Hilbert space H(K), and (3) K ha...

We use a tensor product based multi-linear algebra theory to formulate three-dimensional Hilbert space-filling curves. A 3-D Hilbert space-filling curve is specified as a permutation which rearranges threedimensional n n n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing a 3-D Hilbert space-filling curve. Th...

Description: Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geome...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

Assuming the continuum hypothesis, we show that the Calkin algebra has 2 ℵ 1 outer automorphisms. Let H be a separable infinite dimensional Hilbert space, let L(H) be the algebra of bounded operators on H, let K(H) be the algebra of compact operators on H, and let Q = L(H)/K(H) be the Calkin algebra. A long-standing problem asks whether every automorphism of Q is inner, that is, of the form x →...

A theorem of Bade proves that for a complete Boolean sublattice S£ of 3>(3if) the following holds: SS {PeS£"; P is orthogonal projection operator} We prove that this theorem does not hold for the physically interesting class of non-Boolean propositional systems embedded in a 3>(3if); we derive however a necessary and sufficient condition under which the theorem does hold. This condition is auto...

Publications in Refereed Journals 1. I numeri di Fermat, Periodico di Matematiche, VII, 5 (1998), no. 2-3, 63–68 2. Some observations on the statistical independence and the distribution of zeros in the Selberg Class, Rend. Circ. Mat. Palermo (2), 52 (2003), no. 2, 211–223 3. Extending the idea of compressed algebra to arbitrary socle-vectors, J. Algebra 270 (2003), no. 1, 181–198 4. When are T...