Norm Properties of $S$-Universal Operators
We investigate the norm properties of a generalized derivation on a norm ideal $\mathcal{J}$ in $\mathcal{B}(H)$, the algebra of bounded linear operators on a Hilbert space $H$. Specifically, we extend the concept of $S-$universality from the inner derivation to the generalized derivation context, e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2020-06-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1177851 |
| _version_ | 1797294140841525248 |
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| author | Joshua Muholo Job Bonyo |
| author_facet | Joshua Muholo Job Bonyo |
| author_sort | Joshua Muholo |
| collection | DOAJ |
| description | We investigate the norm properties of a generalized derivation on a norm ideal $\mathcal{J}$ in $\mathcal{B}(H)$, the algebra of bounded linear operators on a Hilbert space $H$. Specifically, we extend the concept of $S-$universality from the inner derivation to the generalized derivation context, establish the necessary conditions for the attainment of the optimal value of the circumdiameters of numerical ranges and the spectra of two bounded linear operators on $H$. Moreover, we characterize the antidistance from an operator to its similarity orbit in terms of the circumdiameters, norms, numerical and spectra radii of a pair of $S$-universal operators. |
| first_indexed | 2024-03-07T21:25:56Z |
| format | Article |
| id | doaj.art-80e0dba6199f44cabec84c0077579cfb |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:25:56Z |
| publishDate | 2020-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-80e0dba6199f44cabec84c0077579cfb2024-02-27T04:36:37ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012020-06-013282901225Norm Properties of $S$-Universal OperatorsJoshua Muholo0Job Bonyo1MASENO UNIVERSITYMASENO UNIVERSITYWe investigate the norm properties of a generalized derivation on a norm ideal $\mathcal{J}$ in $\mathcal{B}(H)$, the algebra of bounded linear operators on a Hilbert space $H$. Specifically, we extend the concept of $S-$universality from the inner derivation to the generalized derivation context, establish the necessary conditions for the attainment of the optimal value of the circumdiameters of numerical ranges and the spectra of two bounded linear operators on $H$. Moreover, we characterize the antidistance from an operator to its similarity orbit in terms of the circumdiameters, norms, numerical and spectra radii of a pair of $S$-universal operators.https://dergipark.org.tr/tr/download/article-file/1177851spectrumnumerical rangecircumdiametersimilarity orbitantidistancenorms;norm idealsnormaloidspectraloid operators |
| spellingShingle | Joshua Muholo Job Bonyo Norm Properties of $S$-Universal Operators Communications in Advanced Mathematical Sciences spectrum numerical range circumdiameter similarity orbit antidistance norms; norm ideals normaloid spectraloid operators |
| title | Norm Properties of $S$-Universal Operators |
| title_full | Norm Properties of $S$-Universal Operators |
| title_fullStr | Norm Properties of $S$-Universal Operators |
| title_full_unstemmed | Norm Properties of $S$-Universal Operators |
| title_short | Norm Properties of $S$-Universal Operators |
| title_sort | norm properties of s universal operators |
| topic | spectrum numerical range circumdiameter similarity orbit antidistance norms; norm ideals normaloid spectraloid operators |
| url | https://dergipark.org.tr/tr/download/article-file/1177851 |
| work_keys_str_mv | AT joshuamuholo normpropertiesofsuniversaloperators AT jobbonyo normpropertiesofsuniversaloperators |