| Title: | On commutators of idempotents |
|---|
| Authors: | ID Drnovšek, Roman (Author) |
|---|
| Files: |  PDF - Presentation file, download (906,25 KB)
MD5: 62463D90DC9A6452EEB47ED554094D6F
 URL - Source URL, visit https://www.tandfonline.com/doi/full/10.1080/03081087.2024.2368734
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | Let $T$ be an operator on Banach space $X$ that is similar to $- T$ via an involution $U$. Then $U$ decomposes the Banach space $X$ as $X = X_1 \oplus X_2$ with respect to which decomposition we have $U = \left(\begin{matrix} I_1 & 0 \\ 0 & -I_2 \end{matrix} \right)$, where $I_i$ is the identity operator on the closed subspace $X_i$ ($i=1, 2$). Furthermore, $T$ has necessarily the form $T = \left(\begin{matrix} 0 & * \\ * & 0 \end{matrix} \right) $ with respect to the same decomposition. In this note we consider the question when $T$ is a commutator of the idempotent $P = \left(\begin{matrix} I_1 & 0 \\ 0 & 0 \end{matrix} \right)$ and some idempotent $Q$ on $X$. We also determine which scalar multiples of unilateral shifts on $l^p$ spaces ($1 \le p \le \infty$) are commutators of idempotent operators. |
|---|
| Keywords: | Banach spaces, operators, idempotents, commutators |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.01.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 649-654 |
|---|
| Numbering: | Vol. 73, iss. 4 |
|---|
| PID: | 20.500.12556/DiRROS-22107  |
|---|
| UDC: | 517.9 |
|---|
| ISSN on article: | 0308-1087 |
|---|
| DOI: | 10.1080/03081087.2024.2368734 |
|---|
| COBISS.SI-ID: | 233159171 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 24.04.2025 |
|---|
| Views: | 478 |
|---|
| Downloads: | 260 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
