Symmetric Invariant Subspaces of Complexifications of Linear Operators

TL;DR

This paper proves the existence of invariant subspaces for certain operators in real Banach spaces, including linear isometries, advancing understanding of operator structure in functional analysis.

Contribution

It establishes the existence of invariant subspaces for specific classes of operators in real Banach spaces, such as linear isometries.

Findings

Linear isometries have invariant subspaces.

Existence of invariant subspaces proven for some operators in real Banach spaces.

Advances understanding of operator structure in functional analysis.

Abstract

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces