The local multiplier algebra of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math>-algebra with finite dimensional irreducible representations

Gogić, Ilja

doi:10.1016/j.jmaa.2013.06.036

Cited by 5 publications

(3 citation statements)

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“…We first show that there is a dense open subset U of X such that Ȟ2 (U ; Z) = 0. This can be shown by using the similar arguments as in the proof of [15,Lemma 3.1]. Indeed, let F be a collection of all families V consisting of mutually disjoint open contractable subsets of X.…”

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confidence: 84%

The cb-norm approximation of generalized skew derivations by elementary operators

Gogić

2019

Preprint

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Let A be a ring and σ : A → A a ring endomorphism. A generalized skew (or σ-)derivation of A is an additive map d : A → A for which there exists a map δ :algebra and σ is surjective, we determine the structure of generalized σ-derivations of A that belong to the cb-norm closure of elementary operators Eℓ(A) on A; all such maps are of the form d(x) = bx + axc for suitable elements a, b, c of the multiplier algebra M (A). As a consequence, if an epimorphism σ : A → A lies in the cb-norm closure of Eℓ(A), then σ must be an inner automorphism. We also show that these results cannot be extended even to relatively well-behaved non-prime C * -algebras like C(X, M 2 ).

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confidence: 84%

The cb-norm approximation of generalized skew derivations by elementary operators

Gogić

2019

Preprint

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“…G.K. Pedersen proved that for a separable C * -algebra A every derivation on A extends to an inner derivation of M loc (A) (see [27]). There are some recent extensions of these results due to D.W. Somerset [35] and I. Gogić [16,17]. But much less seems to be known about proper extensions of Sakai, i.e.…”

Section: Inner Derivations Determined By Elements In the Multiplier Amentioning

confidence: 97%

Inner Derivations and Weak-2-Local Derivations on the $$\hbox {C}^*$$ C ∗ -Algebra $$\varvec{C_0(L,A)}$$

Jordá

Peralta

2017

Integr. Equ. Oper. Theory

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Let L be a locally compact Hausdorff space. Suppose A is a C *-algebra with the property that every weak-2-local derivation on A is a (linear) derivation. We prove that every weak-2-local derivation on C 0 (L, A) is a (linear) derivation. Among the consequences we establish that if B is an atomic von Neumann algebra or on a compact C *-algebra, then every weak-2-local derivation on C 0 (L, B) is a linear derivation. We further show that, for a general von Neumann algebra M , every 2-local derivation on C 0 (L, M) is a linear derivation. We also prove several results representing derivations on C 0 (L, B(H)) and on C 0 (L, K(H)) as inner derivations determined by multipliers.

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“…Therefore J wc (A) = {0}, as with the rotation algebra. On the other hand, if A is a C * -algebra for which all irreducible representations have finite dimension, then it follows from [24,Corollary 3.8] that the ideal J wc (A) is essential.…”

Section: Page 10 Of 40 Manuscript Submitted To International Mathematics Research Noticesmentioning

confidence: 99%

The Centre-Quotient Property and Weak Centrality forC*-Algebras

Archbold

Gogić

2020

International Mathematics Research Notices

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We give a number of equivalent conditions (including weak centrality) for a general $C^*$-algebra to have the centre-quotient property. We show that every $C^*$-algebra $A$ has a largest weakly central ideal $J_{wc}(A)$. For an ideal $I$ of a unital $C^*$-algebra $A$, we find a necessary and sufficient condition for a central element of $A/I$ to lift to a central element of $A$. This leads to a characterisation of the set $V_A$ of elements of an arbitrary $C^*$-algebra $A$, which prevent $A$ from having the centre-quotient property. The complement $\textrm{CQ}(A):= A \setminus V_A$ always contains $Z(A)+J_{wc}(A)$ (where $Z(A)$ is the centre of $A$), with equality if and only if $A/J_{wc}(A)$ is abelian. Otherwise, $\textrm{CQ}(A)$ fails spectacularly to be a $C^*$-subalgebra of $A$.

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The local multiplier algebra of aC∗-algebra with finite dimensional irreducible representations

Cited by 5 publications

References 14 publications

The cb-norm approximation of generalized skew derivations by elementary operators

The cb-norm approximation of generalized skew derivations by elementary operators

Inner Derivations and Weak-2-Local Derivations on the $$\hbox {C}^*$$ C ∗ -Algebra $$\varvec{C_0(L,A)}$$

The Centre-Quotient Property and Weak Centrality forC*-Algebras

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