Chapter 4 Dominated Operators Page 1 Chapter 4 Dominated Operators Dominated operators
are frequent in analysis. The most familiar examples are the Bochner integral, the conditional …

The subject of the present book is sub differential calculus. The main source of this branch of
functional analysis is the theory of extremal problems. For a start, we explicate the origin and …

Boolean valued analysis is a technique for studying properties of an arbitrary mathematical
object by comparing its representations in two different set-theoretic models whose …

Humans definitely feel truth but cannot define truth properly. That is what Alfred Tarski
explained to us in the 1930s. Mathematics pursues truth by way of proof, as wittily phrased …

The notion of equality between two observables will play many important roles in
foundations of quantum theory. However, the standard probabilistic interpretation based on …

The aim of this paper is to give a complete classification of type IAW*-algebras using
Boolean valued analysis. The structure theory of type I AW*-algebras was instituted by …

In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean
valued models of set theory by constructing a model of set theory based on quantum logic …

Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for
studying the properties of an arbitrary mathematical object by discriminating between its …

Рассматриваются непрерывные банаховы расслоения над экстремально несвязными
компактами. Вводятся и исследуются понятия просторного непрерывного банахова …

Recently, systematic applications of the Scott-Solovay Boolean valued set theory were done
by several authors; Takeuti [25, 26, 27, 28, 29, 30], Nishimura [13, 14] Jech [8] and Ozawa …