• Title/Summary/Keyword: Multiplier algebra

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DILATION OF PROJECTIVE ISOMETRIC REPRESENTATION ASSOCIATED WITH UNITARY MULTIPLIER

  • Im, Man Kyu;Ji, Un Cig;Kim, Young Yi;Park, Su Hyung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.367-373
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    • 2007
  • For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.

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A NOTE ON MULTIPLIERS OF AC-ALGEBRAS

  • Lee, Yong Hoon
    • Journal of the Chungcheong Mathematical Society
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    • v.30 no.4
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    • pp.357-367
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    • 2017
  • In this paper, we introduce the notion of multiplier of AC-algebra and consider the properties of multipliers in AC-algebras. Also, we characterized the fixed set $Fix_d(X)$ by multipliers. Moreover, we prove that M(X), the collection of all multipliers of AC-algebras, form a semigroup under certain binary operation.

ON MULTIPLIERS ON BOOLEAN ALGEBRAS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.4
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    • pp.613-629
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    • 2016
  • In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

A NEW PROOF OF MACK'S CHARACTERIZATION OF PCS-ALGEBRAS

  • Kim, Hyoung-Soon;Woo, Seong-Choul
    • Communications of the Korean Mathematical Society
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    • v.18 no.1
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    • pp.59-63
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    • 2003
  • Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

STABLE RANKS OF MULTIPLIER ALGEBRAS OF C*-ALGEBRAS

  • Sudo, Takahiro
    • Communications of the Korean Mathematical Society
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    • v.17 no.3
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    • pp.475-485
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    • 2002
  • We estimate the stable rank, connected stable rank and general stable rank of the multiplier algebras of $C^{*}$-algebras under some conditions and prove that the ranks of them are infinite. Moreover, we show that for any $\sigma$-unital subhomogeneous $C^{*}$-algebra, its stable rank is equal to that of its multiplier algebra.

ON MULTIPLIER WEIGHTED-SPACE OF SEQUENCES

  • Bouchikhi, Lahcen;El Kinani, Abdellah
    • Communications of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.1159-1170
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    • 2020
  • We consider the weighted spaces ℓp(𝕊, 𝜑) and ℓp(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓp(𝕊, 𝜓) to be multiplier weighted-space of ℓp(𝕊, 𝜑) and ℓp(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓp(ℤ,𝜓) is a convolutive algebra.