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On distinct representatives and mapping theorems

โœ Scribed by Phillip A Ostrand


Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
327 KB
Volume
40
Category
Article
ISSN
0022-247X

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## Abstract We show that, for each orientable surface ฮฃ, there is a constant __c__~ฮฃ~ so that, if __G__~1~ and __G__~2~ are embedded simultaneously in ฮฃ, with representativities __r__~1~ and __r__~2~, respectively, then the minimum number cr(__G__~1~, __G__~2~) of crossings between the two maps sat

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respectively for the spectrum and the Weyl spectrum of T ; moreover, Weyl's ลฝ . theorem holds for f T q F if ''dominant'' is replaced by ''M-hyponormal,'' where F is any finite rank operator commuting with T. These generalize earlier results for hyponormal operators. It is also shown that there exis