Toeplitz and Ces\`aro-Type Operators on Homogeneous Siegel Domains

TL;DR

This paper investigates Toeplitz and Cesàro-type operators on holomorphic function spaces within homogeneous Siegel domains of Type II, establishing conditions for their continuity, compactness, and Schatten class membership.

Contribution

It provides new necessary and sufficient criteria for these operators' properties on such domains, advancing the understanding of their functional analysis.

Findings

Characterization of conditions for operator continuity

Criteria for compactness and Schatten class inclusion

Extension of operator theory to homogeneous Siegel domains

Abstract

In this paper we study Toeplitz and Ces\`aro-type operators on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions for these operators to be continuous or compact, or to belong to suitable Schatten classes.