Spectrum of Class <inline-formula><graphic file="1029-242X-2007-027195-i1.gif"/></inline-formula> Operators
<p/> <p>This paper discusses some spectral properties of class <inline-formula><graphic file="1029-242X-2007-027195-i2.gif"/></inline-formula> operators for <inline-formula><graphic file="1029-242X-2007-027195-i3.gif"/></inline-formula...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2007/027195 |
| Summary: | <p/> <p>This paper discusses some spectral properties of class <inline-formula><graphic file="1029-242X-2007-027195-i2.gif"/></inline-formula> operators for <inline-formula><graphic file="1029-242X-2007-027195-i3.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2007-027195-i4.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2007-027195-i5.gif"/></inline-formula>, and <inline-formula><graphic file="1029-242X-2007-027195-i6.gif"/></inline-formula>. It is shown that if <inline-formula><graphic file="1029-242X-2007-027195-i7.gif"/></inline-formula> is a class <inline-formula><graphic file="1029-242X-2007-027195-i8.gif"/></inline-formula> operator, then the Riesz idempotent <inline-formula><graphic file="1029-242X-2007-027195-i9.gif"/></inline-formula> of <inline-formula><graphic file="1029-242X-2007-027195-i10.gif"/></inline-formula> with respect to each nonzero isolated point spectrum <inline-formula><graphic file="1029-242X-2007-027195-i11.gif"/></inline-formula> is selfadjoint and <inline-formula><graphic file="1029-242X-2007-027195-i12.gif"/></inline-formula>. Afterwards, we prove that every class <inline-formula><graphic file="1029-242X-2007-027195-i13.gif"/></inline-formula> operator has SVEP and property <inline-formula><graphic file="1029-242X-2007-027195-i14.gif"/></inline-formula>, and Weyl's theorem holds for <inline-formula><graphic file="1029-242X-2007-027195-i15.gif"/></inline-formula> when <inline-formula><graphic file="1029-242X-2007-027195-i16.gif"/></inline-formula>.</p> |
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| ISSN: | 1025-5834 1029-242X |