On Normal Operators in Hilbert Space

Putnam, C. R.

doi:10.2307/2372180

Cited by 130 publications

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“…Of course the "only if" implication is obvious. As to the converse, we use the well-known Fuglede-Putnam theorem [7,8] …”

Section: Resultsmentioning

confidence: 99%

On the product of the self‐adjoint operators

Rehder

1982

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the posltlvity requirement cannot be dropped.KEY WORDS AND PHPSES. Self-adjoint given by the so-called "statistical operator". W, which is positive with trace (W) 1 and also named the "density operator" of the system. This probabilistic parlance stems from the intrinsic stochastic nature of quantum mechanics: property a, say, with representing operator A, will be found in the system not with certainty, but with a probability given by PW (a) trace (WA), and by measuring a, the original system changes into a new one whose density or state is given by AWA trace (WA)

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“…Of course the "only if" implication is obvious. As to the converse, we use the well-known Fuglede-Putnam theorem [7,8] …”

Section: Resultsmentioning

confidence: 99%

On the product of the self‐adjoint operators

Rehder

1982

International Journal of Mathematics and Mathematical Sciences

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“…It affirms that if A and B are normal operators and AX = X B for some operator X then A * X = X B * . First, Fuglede [10] proved it in the case when A = B and then Putnam [22] proved it in a general case. There exists many generalizations of this Theorem of which most of them go into unwinding the normality of A and B (see [11,20] and some of the references cited in these papers).…”

Section: Fuglede-putnam Theorem For N-power Normal Operatorsmentioning

confidence: 99%

Fuglede-Putnam Theorem and Quasi-nilpotent part of n-power normal operators

Mary¹,

Vijayalakshmi²

2015

Tamkang J. Math.

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“…It is elementary, though tedious, to produce two 4X4 matrices, N a diagonal and X nonzero in the (1,3), (1,4), (2,3), (2,4) The general question in this section is which of the results of the earlier sections remain true for the infinite sum. The theme is to try to prove Theorem 1 in this setting.…”

Section: Ddme8:l(h)^l(h)bymentioning

confidence: 99%

Untitled

1983

Trans. Amer. Math. Soc.

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On Normal Operators in Hilbert Space

Cited by 130 publications

References 0 publications

On the product of the self‐adjoint operators

On the product of the self‐adjoint operators

Fuglede-Putnam Theorem and Quasi-nilpotent part of n-power normal operators

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