The Solution of the Invariant Subspace Problem. Complex Hilbert space. Part I.External non-Archimedean field {∗}^ℝ_{c}^{#} by Cauchy completion of the internal non-Archimedean field {∗}^ℝ.

Journal of Advances in Mathematics and Computer Science 37 (10):51-89 (2022)
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Abstract

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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Set theory with a Filter quantifier.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (2):263-287.
Realism, nonstandard set theory, and large cardinals.Karel Hrbacek - 2001 - Annals of Pure and Applied Logic 109 (1-2):15-48.

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