DOI QR코드

DOI QR Code

WEIGHTED COMPOSITION OPERATORS BETWEEN LP-SPACES

  • JABBARZADEH, M.R.
  • Published : 2005.05.01

Abstract

In this paper we will consider the weighted composition operator $W=uC_{\varphi}$ between two different $L^p(X,\;\Sigma,\;\mu)$ spaces, generated by measurable and non-singular transformations $\varphi$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\varphi$ that induce weighted composition operators between $L^p-spaces$ by using some properties of conditional expectation operator, pair $(u,\;\varphi)$ and the measure space $(X,\;\Sigma,\;\mu)$. Also, Fredholmness of these type operators will be investigated.ᘀࡠ궚䃨⨀磕ྈ肀Ѐ᠀܀䃨⨀᠀Ѐ쌛ܕ儁돐僧⨀ꣻ⨀ꣻ⨀儈돀룡⨀堘?⨀냑ʗ⨀⤈돐偦඗⨀偦඗⨀唀䩁䭏㈰〵〲㘳㜱㜱㠶㠀

Keywords

weighted composition operator;conditional expectation;multiplication operator;Fredholm operator

References

  1. H. Takagi, Fredholm weighted composition operators, Integral Equations Operator Theory 16 (1993), 267-276 https://doi.org/10.1007/BF01358956
  2. S. Axler, Zero multipliers of Bergman spaces, Canad. Math. Bull. 28 (1985), 237-242 https://doi.org/10.4153/CMB-1985-029-1
  3. J. Campbell and J. Jamison, On some classes of weighted composition operators, Glasg. Math. J. 32 (1990), 87-94 https://doi.org/10.1017/S0017089500009095
  4. T. Hoover, A. Lambert, and J. Quinn, The Markov process determined by a weighted composition operator, Studia Math. Poland, LXXII (1982), 225-235
  5. M. R. Jabbarzadeh and E. Pourreza, A note on weighted composition operators on $L^p$-spaces, Bull. Iranian Math. Soc. 29 (2003), 47-54
  6. B. S. Komal and S. Gupta, Multiplication operators between Orlicz spaces, Integral Equations Operator Theory 41 (2001), 324-330 https://doi.org/10.1007/BF01203174
  7. A. Lambert, Localising sets for sigma-algebras and related point transformations, Proc. Roy. Soc. Edinburgh Ser. A 118 (1991), 111-118
  8. R. K. Singh and J. S. Manhas, Composition operators on function spaces, NorthHolland, 1993
  9. H. Takagi and K. Yokouchi, Multiplication and composition operators between two $L^p$-spaces, Contemp. Math. 232 (1999), 321-338 https://doi.org/10.1090/conm/232/03408
  10. A. E. Taylor and D. C. Lay, introduction to functional analysis, 2nd ed., Wiley, 1980
  11. A. C. Zaanen, Integration, 2nd ed., North-Holland, Amsterdam, 1967

Cited by

  1. Basic properties of multiplication and composition operators between distinct Orlicz spaces vol.30, pp.2, 2017, https://doi.org/10.1007/s13163-016-0214-1