Conditions for Linear Dependence of Two Operators

  • Bojan Kuzma
  • Gorazd Lešnjak
  • Chi-Kwong Li
  • Tatjana Petek
  • Leiba Rodman
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)


The linear dependence property of two Hilbert space operators is expressed in terms of equality of size of values of certain sesquilinear and quadratic forms associated with the operators. The forms are based on qnumerical ranges.


Hilbert space linear operators linear dependence numerical values generalized numerical range 

Mathematics Subject Classification (2000)

Primary 47A12 Secondary 47A99 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Bojan Kuzma
    • 1
  • Gorazd Lešnjak
    • 2
  • Chi-Kwong Li
    • 3
  • Tatjana Petek
    • 4
  • Leiba Rodman
    • 3
  1. 1.Inst. of Mathematics, Physics, and MechanicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Department of Electrical Engineering and Computer ScienceUniversity of MariborMariborSlovenia
  3. 3.Department of MathematicsCollege of William and MaryWilliamsburgUSA
  4. 4.University of MariborFERIMariborSlovenia

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