Keywords

#bounded_operator

Bounded operator

Linear transformation between topological vector spaces

In functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces, then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa.

Tue 16th

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Bounded operator Operator norm Unitary operator Unbounded operator Spectrum (functional analysis) Self-adjoint operator Compact operator Hilbert–Schmidt operator Closed linear operator Operator theory
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