In this paper the concept of unbounded Fredholm operators on Hilbert C∗modules over an arbitrary C∗-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C∗-modules over C∗-algebras of compact operators. In the framework of Hilbert C∗-modules over C∗-algebras of compact operators, the index of an unbounded Fredholm operator and the...

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of and algebra. After it is shown that the axioms are independent, given some properties algebraic structure. Then stated relationship between defining unary operation on Also, presented deductive system ideal It defined an generated subset algebra, constructed new adding element to its ideal.

Let A be a linear bounded operator in a Hilbert space H, N(A) and R(A) its null-space and range, and A∗ its adjoint. The operator A is called Fredholm iff dim N(A) = dim N(A∗) := n < ∞ and R(A) and R(A∗) are closed subspaces of H. A simple and short proof is given of the following known result: A is Fredholm iff A = B + F , where B is an isomorphism and F is a finite-rank operator. The proof co...

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...

In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C∗-algebra and the relationship between the set of all adjointable operators from a Hilbert A -module E to a Hilbert A module F and the set of all adjointable operators from the multiplier module M(E) of E to the multiplier module M(F ) of F.

In this article, we throw a bridge between two objects which are unrelated at rst sight. One is the in nite dimensional Heisenberg algebra (simply the Heisenberg algebra, later) which plays a fundamental role in the representation theory of the a ne Lie algebras. The other is the Hilbert schemes of points on a complex surface appearing in the algebraic geometry. As we will explain soon, the Hei...

Let M be a Banach C*-module over a C*-algebra A carrying two A-valued inner products 〈., .〉1, 〈., .〉2 which induce equivalent to the given one norms on M. Then the appropriate unital C*-algebras of adjointable bounded A-linear operators on the Hilbert A-modules {M, 〈., .〉1} and {M, 〈., .〉2} are shown to be ∗-isomorphic if and only if there exists a bounded A-linear isomorphism S of these two Hi...

In this work we examine generalized Connes-Lott models, with C ⊕ C as finite algebra, over the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure (magnetic monopoles). The finitely generated projective module over the full algebra is also taken as topologically non-trivial, wh...

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over C. We also show that the chiral WZW model of a simply c...