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Unit 21: The Conjugate of an Operator

2. Let T be an operator on a normed linear space N. If N is considered to be part of N** by Notes
means of the natural imbedding. Show that T** is an extension of T. Observe that if N is
reflexive, then T** = T.
3. Let T be an operator on a Banach space B. Show that T has an inverse T T* has an inverse
–1
–1
–1
–1
(T*) , and that in this case (T*) = (T )*.
21.5 Further Readings

Books James Wilson Daniel, The Conjugate Gradient Method for Linear and Non-linear
Operator Equations.
G.O. Okikiolu, Special Integral Operators: Poisson Operators, Conjugate Operators and
related Integrals. Vol. Okikiolu Scientific and Industrial Organization, 1981.

Online links epubs.siam-org/sinum/resource/1/sjnamm/v9/i|/p165_s|
www.ima.umm.edu

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