| URN |
etd-0709107-162359 |
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| Author |
Chih-jen Wang |
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| Author's Email Address |
No Public. |
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| Statistics |
This thesis had been viewed 5182 times. Download 1123 times. |
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| Department |
Applied Mathematics |
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| Year |
2006 |
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| Semester |
2 |
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| Degree |
Master |
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| Type of Document |
|
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| Language |
English |
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| Title |
On the invertibility of linear sums of two
idempotents and of two square zero operators |
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| Date of Defense |
2007-06-15 |
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| Page Count |
35 |
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| Keyword |
partial isometry
idempotent
n-potent
invertibility
nilpotent
square-zero operator
|
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| 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. |
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| 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
|
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| Files |
indicate accessible in a year |
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| Date of Submission |
2007-07-09 |
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