In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

In this paper we define a notion of Witt group for sesquilinear forms in hermitian categories, which in turn provides a notion of Witt group for sesquilinear forms over rings with involution. We also study the extension of scalars for K-linear hermitian categories, where K is a field of characteristic 6= 2. We finally extend several results concerning sesquilinear forms to the setting of system...

In recent work on some topological problems (7), I was forced to adopt a complicated definition of 'Hermitian form' which differed from any in the literature. A recent paper by Tits (5) on quadratic forms over division rings contains a new and simple definition of these. A major objective of this paper is to formulate both these definitions in somewhat more general terms, and to show that they ...

In this paper a variational version of the Trotter-Kato theorem is applied to an innnitesimal generator A of a C 0-semigroup in a Hilbert space that is assumed to be the sum of two linear operators A and B deened on the intersection of their domains, where A ? !I is m-dissipative for some ! > 0 and B is the generator of an analytic semigroup associated with a bounded V-coercive sesquilinear for...

Non-commutative L-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algeb...

The dot product is an important tool for calculations in Rn. For instance, we can use it to measure distance and angles. However, it doesn’t come from just the vector space structure on Rn – to define it implicitly involves a choice of basis. In Math 67, you may have studied inner products on real vector spaces and learned that this is the general context in which the dot product arises. Now, w...

Suppose 2n + 1 ≥ p + q. In an earlier paper in 2000 we study a certain sesquilinear form (, )π introduced by Jian-Shu Li in 1989. For π in the semistable range of θ(MO(p, q) → MSp2n(R)), if (, )π does not vanish, then it induces a sesquilinear form on θ(π). In another work in 2000 we proved that (, )π is positive semidefinite under a mild growth condition on the matrix coefficients of π. In thi...