Normed BCI-algebras

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I n n a y BCIa g br ,t o lwi o l so o d:V — l e a he f lo ng c ncu i nsh l ,Y, ∈ X ’
z ) ; () ( Y =(} ) ( ) 3 0 } ) 0 z ’0 ; I c () z ( z ≤( ) ( ( ( ) = 1 ( ) Y ) } ; 2 ) ) ; () ≤Yi l s z≤Y za dz} 6 i mp e x¥ n Y≤z . () } ; () Y z= ( z } 4 0= 5( )
sbrci t a a o1 u t t n n e h s l A—Bl I a o is s I I A—CI I ≤l 1 V—B1w e A—BI eoe te oet l +l l hr I , e1 1 n t t i d sh p n a
O — B , t .To a s r c h bo e me to e a t , n r uc he c f ec b t a tt e a v — n i n d f c s we i t od e t onc pt fn r a e so o m nd dit n ei s a c n a BCIa g br . — l e a
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I - le r , e n a ta r ei g≤ b u tn ≤ Yi a do l * : 0 L t nBCIag b aX wed f eap ril d rn i o yp tigx n n yi x y f f . e
o ea o n p o o iin lc luu ,b b ta tn ,t e BCIag b a a ie . Ask o l p r t r i r p s o a ac l s y a sr cig h t - e r rs s l n wn wel ,
s brcin o eln mb r h stetin l ie u ly l u tat fra u es a h r ge n q ai z—Y ≤ l z + I Y a d te o a t I x— I z— I n h
l e r a e iv sia e .Th i tn to fs q e c fpon si o m e ag b a r n etg t d s elmi o in o e u n e o i t n n r d BCIag b a s - le r i s
i t o u e a t e a e r p r is a e i v s i a e . n r d c d. nd isr l t d p o e te n e tg t d x K e wo ds y r :BCIa g b a n r ; o me ・ l e r ; o m n r d BCIa g b a it n e l i - ・ e r ;d s a c ; i t — l m
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a om s ,Y,Z ∈ X xi :V
(C 1 ( Y } z) z ) ; B I)( z ) ( )%( Y =0 (C 2 }( ) Y=0 B I)( z} ) ;
( C 3 X=0 B I) ;
(C 4 。 : ¥ = 0i l s = B I) i ; mp e
( C 5 , B I) l 源自文库 0=0i l sz=0 i mp e .
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I s tt o y t r r hr eba i pe a i nsv z un o it r e to n s t a to n e he r he e a et e sco r to ,i , i n,n e s c i n a d ub r c i n.I fwe c nsd rt e a lsmulan ou l , h n, yg ne a ii g t e rc r c e itc , heBo l a le r o i e h m l i t e sy t e b e r zn h i ha a t rs is t o e n ag b a l c m e nt i g;i on i rm e ey t r tt ft e ,t e o s i o ben fwe c sde r l hef s wo o h m i h n,b bs r c i g,t a tc y a t a tn he l t ie t e y i s a ls e i o i e nl h a to ft e , wi o s m e c r c e itc f h or se t b ih d; fwe c nsd ro y t e l s neo h m o ng t o ha a t rs iso i e n e y smia o t s ft e s bt a to n r a umbe ss t a l st e i p ia i n tb i g v r i l rt ho e o h u r c i n i e ln r e swela h m lc to
§ . No me CIag b a 2 r d B — le r s
D e n to i f ii n 1 L tⅡ b o — e a i e r a u e e a n n n g tv e ln mb r e .A e ss t BCI ag b a X sc l d a -l e r i al e 一 — s tsy n :V ,Y ÷ a if i g x ,z ∈ X
bs rpri ome C —l ba eg e . tio tie a tesmo h (o ai p oet s nn r dB I g r a i n I s ba dt t h o r i h— c ei ae sx v n h i p c
m o o ph c a e a d i v r e i a e o o m e m r i1m g i n e s n m g fa n r d BCI a g b a a es i o m e — l e r r tl n r d BCI a g b a . l - l e r s Th e a i n f n r a e r pe t e t e e r l t o s o o m l d p o r i s be we n BCI a g b a a d Ca t sa r d c fBCI . le r n re in p o u to .
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