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      Weighted composition operators on weighted spaces of vector-valued analytic functions

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      https://www.riss.kr/link?id=A103361688

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      다국어 초록 (Multilingual Abstract)

      Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G,E) and HV0 (G,E) be the weighted locally convex spaces of vector-...

      Let V be an arbitrary system of weights on an open connected
      subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of
      all bounded linear operators on a Banach space E. Let HVb (G,E) and
      HV0 (G,E) be the weighted locally convex spaces of vector-valued analytic
      functions. In this paper, we characterize self-analytic mappings
      φ : G → G and operator-valued analytic mappings Ψ : G → B (E) which
      generate weighted composition operators and invertible weighted composition
      operators on the spaces HVb (G,E) and HV0 (G,E) for different
      systems of weights V on G. Also, we obtained compact weighted composition
      operators on these spaces for some nice classes of weights.

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      다국어 초록 (Multilingual Abstract)

      Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G,E) and HV0 (G,E) be the weighted locally convex spaces of vect...

      Let V be an arbitrary system of weights on an open connected
      subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of
      all bounded linear operators on a Banach space E. Let HVb (G,E) and
      HV0 (G,E) be the weighted locally convex spaces of vector-valued analytic
      functions. In this paper, we characterize self-analytic mappings
      φ : G → G and operator-valued analytic mappings Ψ : G → B (E) which
      generate weighted composition operators and invertible weighted composition
      operators on the spaces HVb (G,E) and HV0 (G,E) for different
      systems of weights V on G. Also, we obtained compact weighted composition
      operators on these spaces for some nice classes of weights.

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      참고문헌 (Reference)

      1 K. D. Bierstedt, "Weighted spaces of holomorphic functions on balanced domains" 40 (40): 271-297, 1993

      2 A. Siskakis, "Weighted composition semigroups on Hardy spaces, Proceedings of the symposium on operator theory (Athens, 1985)" 84 : 359-371, 1986

      3 J. S. Manhas, "Weighted composition operators on weighted locally convex spaces of analytic functions" 29 (29): 127-140, 2005

      4 A. Montes-Rodriguez, "Weighted composition operators on weighted Banach spaces of analytic functions" 61 (61): 872-884, 2000

      5 S. Ohno, "Weighted composition operators on the Bloch space" 63 (63): 177-185, 2001

      6 M. D. Contreras, "Weighted composition operators on Hardy spaces" 263 (263): 224-233, 2001

      7 G. Mirzakarimi, "Weighted composition operators on Bergman and Dirichlet spaces" 4 (4): 373-383, 1997

      8 M. D. Contreras, "Weighted composition operators in weighted Banach spaces of analytic functions" 69 (69): 41-60, 2000

      9 S. Ohno, "Weighted composition operators between H∞ and the Bloch space" 5 (5): 555-563, 2001

      10 S. Ohno, "Weighted composition operators between Bloch-type spaces" 33 (33): 191-215, 2003

      1 K. D. Bierstedt, "Weighted spaces of holomorphic functions on balanced domains" 40 (40): 271-297, 1993

      2 A. Siskakis, "Weighted composition semigroups on Hardy spaces, Proceedings of the symposium on operator theory (Athens, 1985)" 84 : 359-371, 1986

      3 J. S. Manhas, "Weighted composition operators on weighted locally convex spaces of analytic functions" 29 (29): 127-140, 2005

      4 A. Montes-Rodriguez, "Weighted composition operators on weighted Banach spaces of analytic functions" 61 (61): 872-884, 2000

      5 S. Ohno, "Weighted composition operators on the Bloch space" 63 (63): 177-185, 2001

      6 M. D. Contreras, "Weighted composition operators on Hardy spaces" 263 (263): 224-233, 2001

      7 G. Mirzakarimi, "Weighted composition operators on Bergman and Dirichlet spaces" 4 (4): 373-383, 1997

      8 M. D. Contreras, "Weighted composition operators in weighted Banach spaces of analytic functions" 69 (69): 41-60, 2000

      9 S. Ohno, "Weighted composition operators between H∞ and the Bloch space" 5 (5): 555-563, 2001

      10 S. Ohno, "Weighted composition operators between Bloch-type spaces" 33 (33): 191-215, 2003

      11 A. Galbis, "Weighted Banach spaces of entire functions" 62 (62): 58-64, 1994

      12 K. De Leeuw, "The isometries of some function spaces" 694-698, 1960

      13 P.-K. Lin, "The isometries of H∞(E)" 143 (143): 69-77, 1990

      14 F. Forelli, "The isometries of Hp" 16 : 721-728, 1964

      15 M. Cambern, "The isometries of H1H" 205-214, 1989

      16 C. J. Kolaski, "Surjective isometries of weighted Bergman spaces" 652-657, 1989

      17 S. Ohno, "Some properties of weighted composition operators on algebras of analytic functions" 2 (2): 369-380, 2001

      18 W. Lusky, "On weighted spaces of harmonic and holomorphic functions" 51 (51): 309-320, 1995

      19 W. Lusky, "On the structure of Hv0(D) and hv0(D)" 159 : 279-289, 1992

      20 J. S. Manhas, "Multiplication operators on weighted locally convex spaces of vector-valued analytic functions" 27 (27): 649-66, 2003

      21 M. Nagasawa, "Isomorphisms between commutative Banach algebras with an application to rings of analytic functions" 11 : 182-188, 1959

      22 R. K. Singh, "Invertible composition operators on weighted function spaces" 59 (59): 489-501, 1994

      23 F. Jafari, "Holomorphic flows, cocycles, and coboundaries" 44 (44): 239-253, 1997

      24 J. B. Conway, "Functions of One Complex Variable, Second edition. Graduate Texts in Mathematics" Springer-Verlag 11-, 1978

      25 W. Rudin, "Functional Analysis" McGraw-Hill Book Co. 1973

      26 B. D. MacCluer, "Essential norms of weighted composition operators between Bloch-type spaces" 33 (33): 1437-1458, 2003

      27 J. Bonet, "Composition operators between weighted Banach spaces of analytic functions" 64 (64): 101-118, 1998

      28 C. Cowen, "Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics" CRC Press 1995

      29 R. K. Singh, "Composition Operators on Function Spaces, North-Holland Mathematics Studies" North-Holland Publishing Co. 179-, 1993

      30 J. H. Shapiro, "Composition Operators and Classical Function Theory" Springer-Verlag 1993

      31 M. D. Contreras, "Compact-type operators defined on H∞, Function spaces (Edwardsville, IL, 1998)" Amer. Math. Soc. 232 : 111-118, 1999

      32 T. Mazur, "Canonical isometry on weighted Bergman spaces" 136 (136): 303-310, 1989

      33 J. B. Garnett, "Bounded Analytic Functions" Academic Press, Inc. 1981

      34 K. D. Bierstedt, "Biduals of weighted Banach spaces of analytic functions" 54 (54): 70-79, 1993

      35 K. D. Bierstedt, "Associated weights and spaces of holomorphic functions" 127 (127): 137-168, 1998

      36 K. D. Bierstedt, "A projective description of weighted inductive limits" 272 (272): 107-160, 1982

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