Diferencia entre revisiones de «Espectro de un operador»

 

*Richtmyer, Robert D. (1978): ''Principles of advanced mathematical physics'', Springer-Verlag, New York, ISBN 0-387-08873-3.

 

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The converse is true if one introduces the additional assumption that ''T'' is closed. By the [[closed graph theorem]], if ''T - λ'': ''D'' &rarr; ''X'' is bijective, then its (algebraic) inverse map is necessarily a bounded operator. (Notice the completeness of ''X'' is required in invoking the closed graph theorem.) Therefore, in contrast to the bounded case, the condition that a complex number ''λ'' lie in the spectrum of ''T'' becomes a purely algebraic one: for a closed <math>T</math>, <math>\lambda</math> is in the spectrum of <math>T</math> if and only if <math>T-\lambda</math> is not bijective.

 

 

 

 

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