# On 2-local *-automorphisms and 2-local isometries of B(H)

## TL;DR

This paper strengthens Semrl's result by showing that 2-local *-automorphisms of B(H) are necessarily *-automorphisms, using a simplified single-equation characterization.

## Contribution

It introduces a unified single-equation condition that characterizes 2-local *-automorphisms, simplifying the previous two-equation approach.

## Key findings

- 2-local *-automorphisms are *-automorphisms
- Single-equation characterization is sufficient
- Strengthens previous automorphism classification

## Abstract

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms.