메뉴 건너뛰기




Volumn 109, Issue 1-2, 2005, Pages 1-14

On the nonnegativity of operator products

Author keywords

Friedrichs extension; Kre n von Neumann extension; Nonnegative operator; Product of operators; Selfadjoint operator; Symmetric operator

Indexed keywords


EID: 27844444306     PISSN: 02365294     EISSN: 15882632     Source Type: Journal    
DOI: 10.1007/s10474-005-0231-x     Document Type: Review
Times cited : (26)

References (25)
  • 1
    • 30244548731 scopus 로고
    • Positive selfadjoint extensions of positive symmetric operators
    • T. Ando and K. Nishio, Positive selfadjoint extensions of positive symmetric operators, Tôhoku Math. J., 22 (1970), 65-75.
    • (1970) Tôhoku Math. J. , vol.22 , pp. 65-75
    • Ando, T.1    Nishio, K.2
  • 2
    • 0141952639 scopus 로고    scopus 로고
    • On the class of extremal extensions of a nonnegative operator
    • B. Sz.-Nagy memorial volume
    • Yu. M. Arlinskiǐ, S. Hassi, H. S. V. de Snoo and Z. Sebestyén, On the class of extremal extensions of a nonnegative operator, Oper. Theory: Adv. Appl. (B. Sz.-Nagy memorial volume), 127 (2001), 41-81.
    • (2001) Oper. Theory: Adv. Appl. , vol.127 , pp. 41-81
    • Arlinskiǐ, Yu.M.1    Hassi, S.2    De Snoo, H.S.V.3    Sebestyén, Z.4
  • 3
    • 84976071216 scopus 로고
    • Products of positive operators
    • S. J. Bernau, Products of positive operators, Proc. Cambridge Phil. Soc., 76 (1974), 415-416.
    • (1974) Proc. Cambridge Phil. Soc. , vol.76 , pp. 415-416
    • Bernau, S.J.1
  • 4
    • 0002035328 scopus 로고
    • Quasi-hermitian operators
    • (Israel, 1960), Jerusalem Academic Press (Jerusalem)
    • J. A. Dieudonné, Quasi-hermitian operators, Proc. Inter. Symp. Linear Algebra (Israel, 1960), Jerusalem Academic Press (Jerusalem, 1961), 115-122.
    • (1961) Proc. Inter. Symp. Linear Algebra , pp. 115-122
    • Dieudonné, J.A.1
  • 5
    • 84968496765 scopus 로고
    • On majorization, factorization, and range inclusion of operators on Hubert space
    • R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hubert space, Proc. Amer. Math. Soc., 17 (1966), 413-415.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 413-415
    • Douglas, R.G.1
  • 6
    • 27844531670 scopus 로고
    • Zur Theorie der Integralgleichung dritter Art
    • A. Garbe, Zur Theorie der Integralgleichung dritter Art, Math. Ann., 76 (1915), 527-547.
    • (1915) Math. Ann. , vol.76 , pp. 527-547
    • Garbe, A.1
  • 7
    • 7444232462 scopus 로고    scopus 로고
    • On Kreǐn's extension theory of nonnegative operators
    • S. Hassi, M. M. Malamud and H. S. V. de Snoo, On Kreǐn's extension theory of nonnegative operators, Math. Nachr., 274/275 (2004), 40-73.
    • (2004) Math. Nachr. , vol.274-275 , pp. 40-73
    • Hassi, S.1    Malamud, M.M.2    De Snoo, H.S.V.3
  • 9
    • 0000727733 scopus 로고
    • Compact linear operators on functional spaces with two norms
    • Ukrainian
    • M. G. Kreǐn, Compact linear operators on functional spaces with two norms, Zbirnik Praz' Instituta Matem. Akad. Nauk URSR, 9 (1947), 104-129 (Ukrainian)
    • (1947) Zbirnik Praz' Instituta Matem. Akad. Nauk URSR , vol.9 , pp. 104-129
    • Kreǐn, M.G.1
  • 10
    • 0032411774 scopus 로고    scopus 로고
    • English translation
    • (English translation: Integral Equations Operator Theory, 30 (1998), 140-162).
    • (1998) Integral Equations Operator Theory , vol.30 , pp. 140-162
  • 11
    • 84980073486 scopus 로고
    • Symmetrizable linear transformations
    • P. D. Lax, Symmetrizable linear transformations, Comm. Pure Appl. Math., 7 (1954), 633-647.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 633-647
    • Lax, P.D.1
  • 12
    • 20144375220 scopus 로고
    • Valeurs singuliéres d'une equation de Fredholm
    • J. Marty, Valeurs singuliéres d'une equation de Fredholm, C.R. Acad. Sci. Paris, 150 (1910), 1499-1502.
    • (1910) C.R. Acad. Sci. Paris , vol.150 , pp. 1499-1502
    • Marty, J.1
  • 13
    • 20144367608 scopus 로고
    • Applications of biorthogonal systems of functions to the theory of integral equations
    • A. J. Pell, Applications of biorthogonal systems of functions to the theory of integral equations, 'Trans. Amer: Math. Soc., 12 (1911), 165-180.
    • (1911) Trans. Amer: Math. Soc. , vol.12 , pp. 165-180
    • Pell, A.J.1
  • 14
    • 7444240715 scopus 로고    scopus 로고
    • Ph.D. dissertation, Department of Applied Analysis, Eötvös Loránd University (Budapest)
    • V. Prokaj, Operator extensions on Hilbert space. Ph.D. dissertation, Department of Applied Analysis, Eötvös Loránd University (Budapest, 1996).
    • (1996) Operator Extensions on Hilbert Space
    • Prokaj, V.1
  • 15
    • 78650536397 scopus 로고
    • Symmetrizable completely continuous linear transformations in Hilbert space
    • W. T. Reid, Symmetrizable completely continuous linear transformations in Hilbert space, Duke Math. J., 18 (1951), 41-56.
    • (1951) Duke Math. J. , vol.18 , pp. 41-56
    • Reid, W.T.1
  • 17
    • 0347690244 scopus 로고
    • Operator extensions on Hilbert space
    • Z. Sebestyén, Operator extensions on Hilbert space, Acta Sci. Math. (Szeged). 57 (1993), 233-248.
    • (1993) Acta Sci. Math. (Szeged) , vol.57 , pp. 233-248
    • Sebestyén, Z.1
  • 18
    • 0013234833 scopus 로고    scopus 로고
    • Positivity of operator products
    • Z. Sebestyén, Positivity of operator products, Acta Sci. Math. (Szeged), 66 (2000), 287-294.
    • (2000) Acta Sci. Math. (Szeged) , vol.66 , pp. 287-294
    • Sebestyén, Z.1
  • 19
    • 0001372868 scopus 로고
    • Restrictions of positive self-adjoint operators
    • Z. Sebestyén and J. Stochel, Restrictions of positive self-adjoint operators, Acta Sci. Math. (Szeged), 55 (1991), 149-154.
    • (1991) Acta Sci. Math. (Szeged) , vol.55 , pp. 149-154
    • Sebestyén, Z.1    Stochel, J.2
  • 20
    • 13744261626 scopus 로고    scopus 로고
    • On products of unbounded operators
    • Z. Sebestyén and J. Stochel, On products of unbounded operators, Acta Math. Hungar., 100 (2003), 105-129.
    • (2003) Acta Math. Hungar. , vol.100 , pp. 105-129
    • Sebestyén, Z.1    Stochel, J.2
  • 21
    • 27844598363 scopus 로고
    • On weakly positive matrices
    • E. P. Wigner, On weakly positive matrices, Canad. J. Math., 15 (1963), 313-317.
    • (1963) Canad. J. Math. , vol.15 , pp. 313-317
    • Wigner, E.P.1
  • 22
    • 84861277645 scopus 로고
    • Über vollstetige symmetrische und symmetrisierbare Operatoren
    • A. C. Zaanen, Über vollstetige symmetrische und symmetrisierbare Operatoren, Nieuw Archiefvoor Wiskunde, 22 (1947), 57-80.
    • (1947) Nieuw Archiefvoor Wiskunde , vol.22 , pp. 57-80
    • Zaanen, A.C.1
  • 23
    • 27844600674 scopus 로고
    • Normalisable transformations in Hubert space and systems of linear integral equations
    • A. C. Zaanen, Normalisable transformations in Hubert space and systems of linear integral equations, Acta Math., 83 (1950), 197-248.
    • (1950) Acta Math. , vol.83 , pp. 197-248
    • Zaanen, A.C.1
  • 25
    • 34250610568 scopus 로고
    • On normalizable transformations in Hubert space
    • H. J. Zimmerberg, On normalizable transformations in Hubert space, Acta Math., 86 (1951), 86-88.
    • (1951) Acta Math. , vol.86 , pp. 86-88
    • Zimmerberg, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.