We introduce a new class of operator algebras on Hilbert space. To each bounded linear operator a spectral algebra is associated. These algebras are quite substantial, each containing the commutant of the associated operator, frequently as a proper subalgebra. We establish several sufficient conditions for a spectral algebra to have a nontrivial invariant subspace. When the associated operator ...

Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...

We consider a class of weak modules for vertex operator algebras that we call logarithmic modules. We also construct nontrivial examples of intertwining operators between certain logarithmic modules for the Virasoro vertex operator algebra. At the end we speculate about some possible logarithmic intertwiners at the level c = 0. Introduction This work is an attempt to explain an algebraic reform...

The structure of 3C-algebra and 5A-algebra constructed by Lam-Yamada-Yamauchi is studied the uniqueness vertex operator algebra these two algebras established. We also give fusion rules for algebras.

In this note we show that an unbounded regular operator t on Hilbert C∗modules over an arbitrary C∗ algebra A has polar decomposition if and only if the closures of the ranges of t and |t| are orthogonally complemented, if and only if the operators t and t∗ have unbounded regular generalized inverses. For a given C∗-algebra A any densely defined A-linear closed operator t between Hilbert C∗-mod...

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here and in [6] that operator algebras with r.c.a.i. should be studied in terms of a certain left ideal of a C∗-algebra. We study operator algebras and their multiplier algebras from the perspective of ‘Hamana theory’ and using the multiplier algebras...

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V . In [DY], it was shown that any irreducible V -module is a completely reducible V module where V G is the G-invariant sub-vertex operator algebra of V . In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V...

We present an exact operator quantization of the Euclidean Black Hole CFT using a recently established free field parametrization of the fundamental fields of the classical theory [4, 5, 6, 7]. Quantizing the map to free fields, we show that the resulting quantum fields are causal and transform as covariant fields w.r.t. the Virasoro algebra. We construct the reflection operator of the quantum ...

We have developed a quantum field theory of spinors based on the algebra canonical anticommutation relations (CAR algebra) Grassmann densities in momentum space. proven existence two spinor vacua. Operators C and T transform normal vacuum into an alternative one, which leads to breaking symmetries. The CPT is real structure operator; it preserves vacuum. that, Dirac Sea, formula for charge conj...