Functions and Analysis

2202 Submissions

[2] viXra:2202.0094 [pdf] submitted on 2022-02-14 23:27:31

Folium of Descartes and Division by Zero Calculus　- 　An Open Question

Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 5 Pages. In this note, in the folium of Descartes, with the division by zero calculus we will see some interesting results at the point at infinity with some interesting geometrical property. We will propose an interesting open question.

In this note, in the folium of Descartes, with the division by zero calculus we will see some interesting results at the point at infinity with some interesting geometrical property. We will propose an interesting open question.
Category: Functions and Analysis

[1] viXra:2202.0040 [pdf] replaced on 2022-02-18 20:40:44

The Solution of the Invariant Subspace Problem Part I. Complex Hilbert space

Authors: Jaykov Foukzon
Comments: 101 Pages.

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory TG.It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence of inaccessible cardinals [1].In this paper we look at a set theory NC_{∞^{#}}^{#}, based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [2]-[5].In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule.We present a new approach to the In this paper we deal with set theory INC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule.We present a new approach to the invariant subspace problem for Hilbert spaces. 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.Non-conservative extension based on set theory NC_{∞}^{} of the model theoretical nonstandard analysis[6] is considered
Category: Functions and Analysis