Alexander J. W.'s A Lemma on Systems of Knotted Curves PDF

By Alexander J. W.

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Extra resources for A Lemma on Systems of Knotted Curves

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9. This implies that A'(W*(A)) is also finite dimensional. Therefore A can be expressed as a direct sum of irreducible operators. V. M. (1957)] and the proof is complete. Now we will describe the necessary and sufficient condition for an operator to be sum of irreducible operators in terms of if-theory language. The main result is the following theorem. 14 Given T£C(H). T is the direct sum of irreducible operators if and only if \J (A'(W* (T)))^^ ®{N ^{00})^ for some ki,k2,0

The sum of diagonal elements in the matrix representation with respect to some ONB. If rankA 0 such that T + Ag(SI) for all AeC(H) with \\A\\ < e.

Tnat r^fc^Irani3,,i = 1,2, • • • , k are pairwise unitarily inequivalent. 7, Pj = 2_^ ®Qij, where Qij£A'(T> ) , {Qij} are pairwise orthogonal, Y^®Qij = ^ anc ^ j Tt \ranQij, j = 1,2, • • • , A; are pairwise unitarily equivalent. Therefore we need only to prove that if A^^B^, l

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A Lemma on Systems of Knotted Curves by Alexander J. W.

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