Linear Operators, Part 2 |
From inside the book
Results 1-3 of 92
Page 2169
... shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) commute and also , as ( v ) shows , satisfy the inequality ( vii ) | ƒ ( T ) | ≤ M sup | ƒ ( ^ ) | . λεσ ( Τ ) These facts show ...
... shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) commute and also , as ( v ) shows , satisfy the inequality ( vii ) | ƒ ( T ) | ≤ M sup | ƒ ( ^ ) | . λεσ ( Τ ) These facts show ...
Page 2179
... show that A - 1 is in ( B ) it is consequently sufficient to show that A1 is in A ( B ) . Thus we may suppose without loss of generality that A is in Ao ( B ) , that is , that A is of the form specified by equations ( i ) , ( ii ) ...
... show that A - 1 is in ( B ) it is consequently sufficient to show that A1 is in A ( B ) . Thus we may suppose without loss of generality that A is in Ao ( B ) , that is , that A is of the form specified by equations ( i ) , ( ii ) ...
Page 2489
Nelson Dunford, Jacob T. Schwartz. ( a ) Show that - | ( Ut — Us ) w | 2 = 2R ( ( U¿ — Us ) w , U¿w ) , wЄ L2 ( μ , Y ) . ( b ) Show that if we L2 ( μ , Y ) and vanishes outside a bounded subset of R , then - | ( U , — U ̧ ) w | 2 ...
Nelson Dunford, Jacob T. Schwartz. ( a ) Show that - | ( Ut — Us ) w | 2 = 2R ( ( U¿ — Us ) w , U¿w ) , wЄ L2 ( μ , Y ) . ( b ) Show that if we L2 ( μ , Y ) and vanishes outside a bounded subset of R , then - | ( U , — U ̧ ) w | 2 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero