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2 B o u n d e d o p e r a t o r s
3 S e m i g r o u p s
4 R e f e r e n c e s
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● R e a d ● E d i t ● V i e w h i s t o r y
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F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
Strong measurability has a number of different meanings, some of which are explained below.
Values in Banach spaces [ edit ]
For a function f Banach space (or Fréchet space ), strong measurability usually means Bochner measurability .
However, if the values of f
L
(
X ,
Y )
{\displaystyle {\mathcal {L}}(X,Y)}
of continuous linear operators from X to Y strong measurability means that the operator f(x ) is Bochner measurable for each fixed x f f uniform measurability (cf. "uniformly continuous " vs. "strongly continuous ").
Bounded operators [ edit ]
A family of bounded linear operators combined with the direct integral is strongly measurable, when each of the individual operators is strongly measurable.
Semigroups [ edit ]
A semigroup of linear operators can be strongly measurable yet not strongly continuous.[1]
References [ edit ]
^ Example 6.1.10 in Linear Operators and Their Spectra, Cambridge University Press (2007) by E.B.Davies
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R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Strongly_measurable_function&oldid=1223599920 " C a t e g o r i e s : ● B a n a c h s p a c e s ● S e m i g r o u p t h e o r y ● A l g e b r a s t u b s H i d d e n c a t e g o r i e s : ● A r t i c l e s n e e d i n g a d d i t i o n a l r e f e r e n c e s f r o m M a y 2 0 2 4 ● A l l a r t i c l e s n e e d i n g a d d i t i o n a l r e f e r e n c e s ● A l l s t u b a r t i c l e s
● T h i s p a g e w a s l a s t e d i t e d o n 1 3 M a y 2 0 2 4 , a t 0 5 : 4 1 ( U T C ) . ● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
