دوره 6، شماره 2 - ( 8-1390 )
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Afshin H, Ranjbar M. On the Decomposition of Hilbert Spaces. IJMSI 2011; 6 (2) :1-7
URL: http://ijmsi.ir/article-1-232-fa.html
URL: http://ijmsi.ir/article-1-232-fa.html
On the Decomposition of Hilbert Spaces. مجله علوم ریاضی و انفورماتیک. 1390; 6 (2) :1-7
چکیده:
Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition for $A$ to be self-conjugate ($A=bar{A}$) is given using a subgroup of H.
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