If ℌ is a normed linear space, a linear operator T: ℌ → ℌ is called bounded if there exists a constant C such that |Tx| ≤ C|x| for all x ∈ ℌ. In this case, the smallest such C is called the operator norm, of T, and is denoted |T|. The boundedness of the operator T is equivalent to its continuity.
KeywordsHilbert Space Orthonormal Basis Compact Operator Compact Space Convergent Subsequence
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