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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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| author | Isabel Marrero |
| author_facet | Isabel Marrero |
| author_sort | Isabel Marrero |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-caaba5be7b9244559ff8030a07c6355d |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-caaba5be7b9244559ff8030a07c6355d2025-08-20T02:59:15ZengMDPI AGMathematics2227-73902025-02-0113574110.3390/math13050741Elementary Operators with <i>m</i>-Null SymbolsIsabel Marrero0Departamento de Análisis Matemático, Universidad de La Laguna (ULL), 38200 La Laguna, SpainMotivated 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.https://www.mdpi.com/2227-7390/13/5/741elementary operator<i>m</i>-isometry<i>m</i>-null operators(<i>m</i>, T)-null operatorsStirling numbers |
| spellingShingle | Isabel Marrero Elementary Operators with <i>m</i>-Null Symbols Mathematics elementary operator <i>m</i>-isometry <i>m</i>-null operators (<i>m</i>, T)-null operators Stirling numbers |
| title | Elementary Operators with <i>m</i>-Null Symbols |
| title_full | Elementary Operators with <i>m</i>-Null Symbols |
| title_fullStr | Elementary Operators with <i>m</i>-Null Symbols |
| title_full_unstemmed | Elementary Operators with <i>m</i>-Null Symbols |
| title_short | Elementary Operators with <i>m</i>-Null Symbols |
| title_sort | elementary operators with i m i null symbols |
| topic | elementary operator <i>m</i>-isometry <i>m</i>-null operators (<i>m</i>, T)-null operators Stirling numbers |
| url | https://www.mdpi.com/2227-7390/13/5/741 |
| work_keys_str_mv | AT isabelmarrero elementaryoperatorswithiminullsymbols |