A Characterization of Strongly Continuous Groups of Linear Operators on a Hilbert Space | Zendy

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A Characterization of Strongly Continuous Groups of Linear Operators on a Hilbert Space

Author(s) -

Liu Kangsheng

Publication year - 2000

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609399006487

Subject(s) - mathematics , hilbert space , resolvent formalism , resolvent , semigroup , bounded operator , bounded function , pure mathematics , characterization (materials science) , mathematical analysis , complex plane , mathematics subject classification , linear operators , banach space , finite rank operator , materials science , nanotechnology

It is proved that the infinitesimal generator A of a strongly continuous semigroup of linear operators on a Hilbert space also generates a strongly continuous group if and only if the resolvent of − A , (λ + A ) −1 , is also a bounded function on some right‐hand‐side half plane of complex numbers, and converges strongly to zero as the real part of λ tends to infinity. An application to a partial differential equation is given. 1991 Mathematics Subject Classification 47D03.

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