Riesz bases and positive operators on Hilbert space
It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product on H in which it is an orthonormal basis, thereby extending the sense in which Riesz bases and orthonormal bases are...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203202349 |
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| _version_ | 1832565138510577664 |
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| author | James R. Holub |
| author_facet | James R. Holub |
| author_sort | James R. Holub |
| collection | DOAJ |
| description | It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product on
H in which it is an orthonormal basis, thereby extending the
sense in which Riesz bases and orthonormal bases are thought of
as being the same. A consequence of the
method of proof of this result yields a series representation for
all positive isomorphisms on a Hilbert space. |
| format | Article |
| id | doaj-art-f7d8beaedcbc4199ad974532dc40230e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f7d8beaedcbc4199ad974532dc40230e2025-02-03T01:09:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003181173117410.1155/S0161171203202349Riesz bases and positive operators on Hilbert spaceJames R. Holub0Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg 24061-0123, VA, USAIt is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product on H in which it is an orthonormal basis, thereby extending the sense in which Riesz bases and orthonormal bases are thought of as being the same. A consequence of the method of proof of this result yields a series representation for all positive isomorphisms on a Hilbert space.http://dx.doi.org/10.1155/S0161171203202349 |
| spellingShingle | James R. Holub Riesz bases and positive operators on Hilbert space International Journal of Mathematics and Mathematical Sciences |
| title | Riesz bases and positive operators on Hilbert space |
| title_full | Riesz bases and positive operators on Hilbert space |
| title_fullStr | Riesz bases and positive operators on Hilbert space |
| title_full_unstemmed | Riesz bases and positive operators on Hilbert space |
| title_short | Riesz bases and positive operators on Hilbert space |
| title_sort | riesz bases and positive operators on hilbert space |
| url | http://dx.doi.org/10.1155/S0161171203202349 |
| work_keys_str_mv | AT jamesrholub rieszbasesandpositiveoperatorsonhilbertspace |