On trace and Hilbert–Schmidt norm estimates
Let ℰ and 풫 be nonnegative quadratic forms in the Hilbert space ℋ. Suppose that, for every β ⩾ 0, the form ℰ+β풫 is densely defined and closed. Let Hβ be the self‐adjoint operator associated with ℰ+β 풫 and R∞ := lim β→∞ (Hβ+1)−1. We give estimates for the distance between (Hβ+1)−1 and R∞ with respect...
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| Veröffentlicht in: | The Bulletin of the London Mathematical Society 2012-08, Vol.44 (4), p.661-674 |
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| container_title | The Bulletin of the London Mathematical Society |
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| creator | BelHadjAli, H. BenAmor, A. Brasche, J. |
| description | Let ℰ and 풫 be nonnegative quadratic forms in the Hilbert space ℋ. Suppose that, for every β ⩾ 0, the form ℰ+β풫 is densely defined and closed. Let Hβ be the self‐adjoint operator associated with ℰ+β 풫 and R∞ := lim β→∞ (Hβ+1)−1. We give estimates for the distance between (Hβ+1)−1 and R∞ with respect to the norm ‖·‖p in the Schatten–von Neumann class of order p, p=1, 2. In particular, we derive a condition that is necessary and sufficient in order that
‖(Hβ + 1)−1 − R∞‖1⩽ c/β∀β > 0
for some finite constant c, and give examples where this criterion is satisfied. |
| doi_str_mv | 10.1112/blms/bdr131 |
| format | Article |
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‖(Hβ + 1)−1 − R∞‖1⩽ c/β∀β > 0
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‖(Hβ + 1)−1 − R∞‖1⩽ c/β∀β > 0
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‖(Hβ + 1)−1 − R∞‖1⩽ c/β∀β > 0
for some finite constant c, and give examples where this criterion is satisfied.</abstract><pub>Oxford University Press</pub><doi>10.1112/blms/bdr131</doi><tpages>14</tpages></addata></record> |
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| title | On trace and Hilbert–Schmidt norm estimates |
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