a
szóközpótlás
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a (szóközpótlás) |
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The spectral theorem can be extended to [[normal operator]]s in general. Therefore the above equality holds for any bounded normal operator ''N''. This formula can sometimes be used to compute the operator norm of a given bounded operator ''A'': define the [[Hermitian operator]] ''H'' = ''A<sup>*</sup>A'', determine its spectral radius, and take the [[square root of a matrix|square root]] to obtain the operator norm of ''A''.
The space of bounded operators on ''H'', with the topology induced by operator norm, is not [[separable space|separable]]. For example, consider the Hilbert space [[Lp space|''L''<sup>2</sup>[0,1]]]. For 0 < ''t'' ≤ 1, let Ω<sub>''t''</sub> be the [[characteristic function]] of [0,''t''], and ''P<sub>t</sub>'' be the [[multiplication operator]] given by Ω<sub>''t''</sub> , i. e.
:<math>P_t (f) = f \cdot \Omega_t .</math>
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