# Operator versions of H\"older inequality and Hilbert $C^*$-modules

## TL;DR

This paper explores operator versions of H"older inequalities within Hilbert $C^*$-modules, extending classical inequalities to operator settings and unitarily invariant norms.

## Contribution

It introduces new operator H"older inequalities based on recent weighted Cauchy-Schwarz results in Hilbert $C^*$-modules.

## Key findings

- Derived new H"older type inequalities for Hilbert space operators
- Extended classical inequalities to the setting of Hilbert $C^*$-modules
- Applied inequalities to unitarily invariant norms

## Abstract

Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.