Spectral Theory
Continuity refers to the property of a function or operator that preserves the limits of sequences, meaning small changes in input lead to small changes in output. This concept is essential in various areas of mathematics and physics, as it ensures stability and predictability in transformations and mappings. In the context of operators on Hilbert spaces, continuity is crucial for understanding how linear transformations behave under convergence, impacting the spectral properties and the structure of these operators.
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