Hypernatural Numbers as Ultrafilters

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers

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

We presen

The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field *Rc#. Part II.

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