Elementary Operators with <i>m</i>-Null Symbols
Motivated by Botelho and Jamison’s seminal 2010 study on elementary operators that are <i>m</i>-isometries, in this paper, we introduce the concept of <i>m</i>-null pairs of operators and establish some structural properties and characterizations of the class of elementary op...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/5/741 |
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| Summary: | Motivated by Botelho and Jamison’s seminal 2010 study on elementary operators that are <i>m</i>-isometries, in this paper, we introduce the concept of <i>m</i>-null pairs of operators and establish some structural properties and characterizations of the class of elementary operators whose symbols are <i>m</i>-null (so-called <i>m</i>-null elementary operators). It is shown that if the symbols of an elementary operator <i>L</i> are, in turn, a <i>p</i>-null elementary operator and a <i>q</i>-null elementary operator, then <i>L</i> is a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-null elementary operator. Some extant results on elementary <i>m</i>-isometries can be recovered from this renewed perspective, often providing added value. |
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| ISSN: | 2227-7390 |