| URN |
etd-0709107-162359 |
|---|
| Author |
Chih-jen Wang |
|---|
| Author's Email Address |
No Public. |
|---|
| Statistics |
This thesis had been viewed 5060 times. Download 1093 times. |
|---|
| Department |
Applied Mathematics |
|---|
| Year |
2006 |
|---|
| Semester |
2 |
|---|
| Degree |
Master |
|---|
| Type of Document |
|
|---|
| Language |
English |
|---|
| Title |
On the invertibility of linear sums of two
idempotents and of two square zero operators |
|---|
| Date of Defense |
2007-06-15 |
|---|
| Page Count |
35 |
|---|
| Keyword |
partial isometry
idempotent
n-potent
invertibility
nilpotent
square-zero operator
|
|---|
| Abstract |
Let P and Q be two idempotents, we review the results about the equivalence between the
invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero
complex numbers with a + b
eq 0. It is possible to extend the results to the case P and Q are
square-zero elements. However, we will show that these extensions are impossible in general
for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q
are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero
a, b. |
|---|
| Advisory Committee |
Mark C. Ho - chair
Mu-Ming Wong - co-chair
Jyh-Shyang Jeang - co-chair
Hwa-Long Gau - co-chair
Ngai-Ching Wong - advisor
|
|---|
| Files |
indicate accessible in a year |
|---|
| Date of Submission |
2007-07-09 |
|---|
