CHARACTERIZATION OF SUM OF ORTHOGONAL PROJECTION OPERATORS ON HILBERT SPACE
An orthogonal projection is a linear transformation which has two properties, idempotent and selfadjoint. This thesis contains characterization of operators which are expressible as a sum of finitely many orthogonal projections on a Hilbert space. In general, the necessary and suffcient condition...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34868 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | An orthogonal projection is a linear transformation which has two properties,
idempotent and selfadjoint. This thesis contains characterization of operators
which are expressible as a sum of finitely many orthogonal projections on a
Hilbert space. In general, the necessary and suffcient conditions of an operator
positive T such that T is expressible as a sum of finitely many of orthogonal
projections is for some Hilbert space N, T o0N is unitarily equivalent to an
operator matrix which diagonal elements are identity operators. In addition,
there also some characterizations of sum of finitely many of orthogonal pro-
jections on infinite dimensional separable Hilbert space based on the essential
norm. A positive operator whose essential norm is less than one is sum of
finitely many orthogonal projections if and only if if it has an integer trace
and its trace is greater than or equal to its rank. |
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