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The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field \(^*\mathbb{R}_c^\#\). Part II.

Jaykov Foukzon

Journal of Advances in Mathematics and Computer Science · pp. 31–69 · Published 6 Dec 2022

10.9734/jamcs/2022/v37i111721

Abstract

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 complex separable Hilbert space H, it follow that T has a non-trivial closed invariant subspace.

Set theory ZFC Nonconservative extension of ZFC Internal set theory IST External set theory HST A. Robinson model theoretical NSA Bivalent gyper infinitary logic Modus ponens rule Logic with restricted modus ponens rule internal non-Archimedean field Invariant subspce problem

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Cited by 2

Basic non-Archimedean functional analysis over a non-Archimedean field ^{∗}ℝ_{c}^{#} Application to constructive quantum field theory

Jaykov Foukzon · 2024

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