Non-self-adjoint resolutions of the identity and associated operators

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity \{X(\lambda)\}_{\lambda\in {\mb R}}, whose adjoints constitute also a resolution of the identity, are studied . In particular, it is shown that a closed operator $B$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $B=TAT^{-1}$ where $A$ is self-adjoint and $T$ is a bounded operator with bounded inverse

Fully representable and *-semisimple topological partial *-algebras

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the \M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea

Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Operators in Rigged Hilbert spaces: some spectral properties

A notion of resolvent set for an operator acting in a rigged Hilbert space \D \subset \H\subset \D^\times is proposed. This set depends on a family of intermediate locally convex spaces living between \D and \D^\times, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.Comment: 29 page

The Effects of Organizational Philanthropic Movements and Related Public Relations Strategies

The following is a comprehensive public relations campaign created after extensive research on public relations efforts and corporate social responsibility. The study is mainly focused on establishing the relationship, if any, between a company’s philanthropic efforts and their profits. The study seeks to answer questions such as “Is the return on investment for philanthropic giving worth it?” and “How might this impact company morale?” With a focus on measuring the success of a philanthropic campaign created for Sereno Group Real Estate company, a small to midsize residential real estate company in the Silicon Valley, this study serves as a basis for understanding philanthropic efforts, where they stemmed from, and the type of impact they might have at the company level as well as even the global level. This text dives into the fundamentals of corporate social responsibility and terms that have evolved due to company’s lack of authenticity when creating these types of movements. Texts such as Yvon Chouinard’s Let My People Go Surfing and Guy Kawasaki’s Art of the Start in addition to personal interviews with industry level top executives are highly integrated into the study’s research, analysis, and conclusions. This study helps define the relationship, if any, between philanthropic public relations strategies and company success defined by public’s perception, company moral and culture, as well as company revenue and profits

Algebraic dynamics in O*-algebras: a perturbative approach

In this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed. The mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasi-uniform topology. After some remarks on the domain of the perturbation, conditions are given for the dynamics to exist as the limit of a net of regularized linear maps