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On the Symbols of Strictly m -Null Elementary Operators

Author

Listed:
  • Isabel Marrero

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

Abstract

This paper extends the previous work by the author on m -null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p -null and q -null, respectively, then L is ( p + q − 1 ) -null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly ( p + q − 1 ) -null, then a scalar λ ≠ 0 exists such that λ A is strictly p -null and λ − 1 B is strictly q -null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m -isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m -isometries and are subsumed by m -null operators, the result is new.

Suggested Citation

  • Isabel Marrero, 2025. "On the Symbols of Strictly m -Null Elementary Operators," Mathematics, MDPI, vol. 13(12), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:2026-:d:1682934
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