In the book that I read, an(adsbygoogle = window.adsbygoogle || []).push({}); operatoris defined to be a linear map which maps from a vector space into itself. For example, if ##T## is an operator in a vector space ##V##, then ##T:V\rightarrow V##. Now, what if I have an operator ##O## such that ##T:V\rightarrow U## where ##U## is a subspace of ##V##. Can I call ##O## an operator in ##V##?

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# Definition of an operator in a vector space

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