Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1010
... norm or the double - norm of T. The class of all Hilbert - Schmidt operators on will be denoted by HS . In this definition of the class HS a particular orthonormal sequence was used . The following lemma shows that the class HS depends ...
... norm or the double - norm of T. The class of all Hilbert - Schmidt operators on will be denoted by HS . In this definition of the class HS a particular orthonormal sequence was used . The following lemma shows that the class HS depends ...
Page 1015
... norm of HS it follows from Lemma VII.6.5 that the contour C of the integral in [ * ] contains σ ( T ) for all suffi- ciently large n . From Corollary VII.6.3 it is seen that , in the norm of HS + , lim [ 2 , -T ] -1 = [ 2 , -T ] -1 N1 ...
... norm of HS it follows from Lemma VII.6.5 that the contour C of the integral in [ * ] contains σ ( T ) for all suffi- ciently large n . From Corollary VII.6.3 it is seen that , in the norm of HS + , lim [ 2 , -T ] -1 = [ 2 , -T ] -1 N1 ...
Page 1297
... norm of ƒ as an element of H ^ ( J ) it follows easily that D ( T1 ( 7 ) ) is also complete under the norm f2 . As f1f it follows from Theorem II.2.5 that the two norms are equivalent . The lemma follows immediately from this ...
... norm of ƒ as an element of H ^ ( J ) it follows easily that D ( T1 ( 7 ) ) is also complete under the norm f2 . As f1f it follows from Theorem II.2.5 that the two norms are equivalent . The lemma follows immediately from this ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero