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Elementary Operators with m -Null Symbols

Author

Listed:
  • Isabel Marrero

    (Departamento de Análisis Matemático, Universidad de La Laguna (ULL), 38200 La Laguna, Spain
    Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), 38200 La Laguna, Spain)

Abstract

Motivated by Botelho and Jamison’s seminal 2010 study on elementary operators that are m -isometries, in this paper, we introduce the concept of m -null pairs of operators and establish some structural properties and characterizations of the class of elementary operators whose symbols are m -null (so-called m -null elementary operators). It is shown that if the symbols of an elementary operator L are, in turn, a p -null elementary operator and a q -null elementary operator, then L is a ( p + q − 1 ) -null elementary operator. Some extant results on elementary m -isometries can be recovered from this renewed perspective, often providing added value.

Suggested Citation

  • Isabel Marrero, 2025. "Elementary Operators with m -Null Symbols," Mathematics, MDPI, vol. 13(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:741-:d:1599002
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