Let H be a separable, infinite dimensional complex Hilbert space and let B(H) be the algebra of bounded linear operators on H. An operator T∈ B(H) is said to be normal if T ∗T = TT ∗, subnormal if T is the restriction of a normal operator (acting on a Hilbert space K ⊇ H) to an invariant subspace, and hyponormal if T ∗T ≥ TT ∗. The Bram-Halmos criterion for subnormality states that an operator ...

Abstract We construct an explicit, multiplicative Chow–Künneth decomposition for the Hilbert scheme of points a K3 surface. further refine this with respect to action Looijenga–Lunts–Verbitsky Lie algebra.

The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentumvector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different values of θ for the θ-term in QCD lagrangian lead to different representations of the Poincare group, which are, however, connected by an unitary transformation...

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be vie...

In this expository paper we present an overview of various graphical categorifications of the Heisenberg algebra and its Fock space representation. We begin with a discussion of “weak” categorifications via modules for Hecke algebras and “geometrizations” in terms of the cohomology of the Hilbert scheme of points on the resolution of a simple singularity. We then turn our attention to more rece...

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras included) with respect to which the multiplication is continuous. 2) Such norms cannot be chosen to be submultiplicative and equal to one on the unit of the algeb...

We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T ) parametrizing Gorenstein Artin algebras with a given Hilbert function T . This gives a lot of examples where Gor(T ) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part with...

We analyze the algebraic structure of the Connes fusion tensor product (CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra M . It turns out that all complications in its definition disappear if one uses the closely related bi-modules of bounded vectors. We construct an equivalence of monoidal categories with duality between a category of Hilbert bi-modules over M with CFT...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

We showed in part I that the Hopf algebra H of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at ε = 0 the holomorphic part γ+(ε) of the Riemann–Hilbert decomposition γ−(ε) γ+(ε) of the loop γ(ε) ∈ G provided by dimensional regularization. We show in ...