The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field \(^*\mathbb{R}_c^\#\). Part II.
Jaykov Foukzon *
Israel Institute of Technology, Haifa, Israel.
*Author to whom correspondence should be addressed.
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.
Keywords: 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