The Solution of the Invariant Subspace Problem in Complex Hilbert Space: External non-Archimedean field *Rc by Cauchy Completion of the internal Non-Archimedean field *R (Part I)
Journal of Advances in Mathematics and Computer Science · pp. 51–89 · Published 23 Nov 2022
10.9734/jamcs/2022/v37i101717Abstract
The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements wich appear as independent of ZFC but which look to be \true". In this paper we deal with set theory NC\(^{\#}{_\infty}_{\#}\) based on hyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC\(^{\#}{_\infty}_{\#}\)contains Aczel's anti-foundation axiom. We present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach based on nonconservative extension of the model theoretical NSA. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional separable complex Hilbert space H;it follow that T has a non-trivial closed invariant subspace.
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Cited by 4
Jaykov Foukzon · Journal of Advances in Mathematics and Computer Science · 2022
Jaykov Foukzon · Journal of Physics: Conference Series · 2024
Showing 2 of 4 known citations — external sources report more than can currently be individually listed.
Related research
- Internal Set Theory IST# Based on Hyper Infinitary Logic with Restricted Modus Ponens Rule: Nonconservative Extension of the Model Theoretical NSA — shares topic coverage
- The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field \(^*\mathbb{R}_c^\#\). Part II. — shares topic coverage
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