Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 91
Page 1180
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L , ( ) , H denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L , ( ) , H denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
Page 1262
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space H12H , and an orthogonal projection Qin , such that Ax = PQx , x = $ , P denoting the orthogonal projection of H1 on H. 29 Let { T } be a sequence of bounded ...
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space H12H , and an orthogonal projection Qin , such that Ax = PQx , x = $ , P denoting the orthogonal projection of H1 on H. 29 Let { T } be a sequence of bounded ...
Page 1773
Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex numbers , together with a complex ... spaces , Hilbert space 1773 APPENDIX REFERENCES NOTATION INDEX AUTHOR INDEX SUBJECT INDEX.
Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex numbers , together with a complex ... spaces , Hilbert space 1773 APPENDIX REFERENCES NOTATION INDEX AUTHOR INDEX SUBJECT INDEX.
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 other sections not shown
Other editions - View all
Common terms and phrases
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