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(i) ユニタリー写像U :V →W とT ∈ B(V)に対して、kU T U∗k=kTkを示せ

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2012/6/21

問1. ２×２実対称行列

T =

a b

b c

のノルムを計算せよ。

問2.

(i) ユニタリー写像U :V →W とT ∈ B(V)に対して、kU T U∗k=kTkを示せ。

(ii) ヒルベルト空間`2(Z)の移動作用素をS で表す。正数a, b, cに対してT =aS+bS2+cS3 のノルム を求めよ。（ヒント：フーリエ変換)

1

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