Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 78
Page 861
... exists , then TT - 1 . Clearly if x - 1 exists then T - 1T , = TT - 1 = I. If T1 exists in B ( X ) , then and if a = xα = x x T ̧ [ ( Tz1y ) z ] = yz , ( T = 1y ) z = T = 1 ( yz ) , T1e , then az = T1z for every z Є X. Also T2a = e = T ...
... exists , then TT - 1 . Clearly if x - 1 exists then T - 1T , = TT - 1 = I. If T1 exists in B ( X ) , then and if a = xα = x x T ̧ [ ( Tz1y ) z ] = yz , ( T = 1y ) z = T = 1 ( yz ) , T1e , then az = T1z for every z Є X. Also T2a = e = T ...
Page 1057
... exists and > 0 ; and the integral ( Vu ) exists and equals P S Ω ( α ) ei ( x , Vu ) dx = P En | x | n S Ω ( Vy ) ei ( v , u ) dy En yn if PpQ ( Vy ) \ y \ " eiv , u ) dy exists and V is a rotation of E " . Thus , to show that the ...
... exists and > 0 ; and the integral ( Vu ) exists and equals P S Ω ( α ) ei ( x , Vu ) dx = P En | x | n S Ω ( Vy ) ei ( v , u ) dy En yn if PpQ ( Vy ) \ y \ " eiv , u ) dy exists and V is a rotation of E " . Thus , to show that the ...
Page 1261
... exists a unique closed linear extension T such that if T , is any closed linear extension of T then TCT1 . T is called the closure of T. 1 ( a ) There exists a densely defined operator with no closed linear extension . ( b ) An operator ...
... exists a unique closed linear extension T such that if T , is any closed linear extension of T then TCT1 . T is called the closure of T. 1 ( a ) There exists a densely defined operator with no closed linear extension . ( b ) An operator ...
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