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Ülger, Ali

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    Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras
    (Institute of Mathematics of the Polish Academy of Sciences, 2007) Kaniuth, Eberhard; Lau, Anthony To-Ming; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism phi : A -> B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and phi) axe given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.
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    The structure of power bounded elements in Fourier-Stieltjes algebras of locally compact groups
    (Elsevier Science Bv, 2013) Kaniuth, Eberhard; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let G be an arbitrary locally compact group and B(G) its Fourier-Stieltjes algebra. An element u of B(G) is called power bounded if sup(n is an element of N) parallel to u(n)parallel to < infinity. We present a detailed analysis of the structure of power bounded elements of B(G) and characterize them in terms of sets in the coset ring of G and w*-convergence of sequences (v(n))(n is an element of N), v is an element of B(G).
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    The phillips properties
    (American Mathematical Society (AMS), 2000) Department of Mathematics; Department of Mathematics; Ülger, Ali; Freedman, Walden; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; N/A
    A Banach space X has the Phillips property if the canonical projection p: X*** → X* is sequentially weak*-norm continuous, and has the weak Phillips property if p is sequentially weak*-weak continuous. We study both properties in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski's properties (u) and (V), and the Schur property. © 2000 by Walden Freedman and Ali Ülger.
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    Relatively weak closed ideals of A(G), sets of synthesis and sets of uniqueness
    (Ars Polona-Ruch, 2014) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are sigma(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C-0(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to the above issues, we present a series of results about closed sets of uniqueness (i.e. closed sets E for which <(J(E))over bar>w* = B(G)).
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    Approximate identities in Banach function algebras
    (Institute of Mathematics of the Polish Academy of Sciences, 2015) Dales, H. G.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples,including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras, We shall describe a contractive Banach function algebra which is not equivalent to a uniform algebra. We shall also obtain results about Banach Sequence algebras and Banach function algebras that are ideals in their second duals.
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    The Rajchman algebra B-0(G) of a locally compact group G
    (Elsevier, 2016) Kaniuth, E.; Lau, A. T.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let G be a locally compact group, B(G) the Fourier-Stieltjes algebra of G and B-0(G) = B(G) boolean and C-0(G). The space B-0(G) is a closed ideal of B(G). In this paper, we study the Banach algebra B-0(G) under various aspects. The main emphasis is on regularity and the existence of various kinds of approximate identities, the question of when the quotient of B-0(G) modulo the Fourier algebra A(G) is radical, the Bochner-Schoenberg-Eberlein property and a characterization of elements in B-0(G) in terms of continuity of translation properties. The paper also contains a number of illustrating examples.
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    When is the range of a multiplier on a Banach algebra closed?
    (Springer, 2006) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    In this paper we prove the Theorem: Let A be a Banach algebra with a bounded approximate identity (=BAI) such that every proper closed ideal of A is contained in a proper closed ideal with a BAI. Then a multiplier T : A -> A has a closed range iff T factors as a product of an idempotent multiplier and an invertible multiplier.
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    Multipliers with closed range on commutative semisimple Banach algebras
    (Polish Acad Sciences Institute Mathematics, 2002) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let A be a commutative semisimple Banach algebra, Delta(A) its Gelfand spectrum, T a multiplier on A and (T) over cap its Gelfand transform. We study the following problems. (a) When is delta(T) = inf {\(T) over cap (f)\ : f is an element of Delta(A), (T) over capT(f) not equal 0} < 0? (b) When is the range T (A) of T closed in A and does it have a bounded approximate identity? (c) How to characterize the idempotent multipliers in terms of subsets of Delta(A)?
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    Arens regularity of the algebra a (circle times) over-cap b (vol 305, pg 623, 1988)
    (American Mathematical Society (AMS), 2003) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
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    A note on the kadison-singer problem
    (Theta Foundation, 2010) Akemann, Charles A.; Tanbay, Betül; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Let H be a separable Hilbert space with a fixed orthonormal basis (e(n)) n >= 1 and B(H) be the full von Neumann algebra of the bounded linear operators T : H -> H. identifying l(infinity) = C(beta N) with the diagonal operators, we consider C(beta N) as a subalgebra of B(H). For each t is an element of beta N, let [delta(t)] be the set of the states of B(H) that extend the Dirac measure delta(t). Our main result shows that, for each t in beta N, the set [delta(t)] either lies in a finite dimensional subspace of B(H)* or else it must contain a homeomorphic copy of beta N.