This is an overview of some techniques of treating the principal objects of functional analysis such as reals, Banach spaces and operators within nonstandard models of set theory.
1. Boolean Valued Prerequisites2. Reals and Boolean Valued Positive Functionals
3. Extension and Decomposition of Positive Operators
4. Differences and Sums of Lattice Homomorphisms 5. Simultaneous Inequalities 6. Interaction with Infinitesimals
REFERENCES
- [1] Kusraev A.G. and Kutateladze S.S. Introduction to Boolean Valued Analysis, Nauka Publishers, Moscow (2005).
- [2] Gordon E. I., Kusraev A. G., and Kutateladze S. S. Infinitesimal Analysis: Selected Topics, Nauka Publishers, Moscow (2011).
This talk was delivered at
the
“
International Conference Dedicated to the 105th Anniversary of the Birthday of Sergei
L. Sobolev” on August 22, 2013, Novosibirsk
Slides in PDF.
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