書誌事項
- 公開日
- 1978-05
- 権利情報
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- https://www.cambridge.org/core/terms
- DOI
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- 10.1017/s0305004100054670
- 公開者
- Cambridge University Press (CUP)
この論文をさがす
説明
<jats:p>One of the most fruitful – and natural – ways of introducing a partial order in the set of bounded self-adjoint operators in a Hilbert space <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" xlink:type="simple" xlink:href="S0305004100054670_xs1D4D7"/> is through the concept of a positive operator. A bounded self-adjoint operator <jats:italic>A</jats:italic> denned on <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" xlink:type="simple" xlink:href="S0305004100054670_xs1D4D7"/> is called positive – and one writes <jats:italic>A</jats:italic> ≥ 0 - if the inner product (ψ, <jats:italic>A</jats:italic>ψ) ≥ 0 for every ψ ∈ <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" xlink:type="simple" xlink:href="S0305004100054670_xs1D4D7"/>. If, in addition, (ψ, <jats:italic>A</jats:italic>ψ) = 0 only if ψ = 0, then A is called <jats:italic>positive-definite</jats:italic> and one writes <jats:italic>A</jats:italic> > 0. Further, if there exists a real number γ > 0 such that <jats:italic>A</jats:italic> — <jats:italic>γI</jats:italic> ≥ 0, <jats:italic>I</jats:italic> being the unit operator, then <jats:italic>A</jats:italic> is called <jats:italic>strictly positive</jats:italic> (in symbols, <jats:italic>A</jats:italic> ≫ 0). In a finite dimensional space, a positive-definite operator is also strictly positive.</jats:p>
収録刊行物
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- Mathematical Proceedings of the Cambridge Philosophical Society
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Mathematical Proceedings of the Cambridge Philosophical Society 83 (3), 393-401, 1978-05
Cambridge University Press (CUP)
