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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Ditkin’s condition and ideals with at most countable hull in algebras of functions analytic in the unit disc

100%
Sołtysiak A., Wawrzyńczyk A.
Commentationes Mathematicae
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2012
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tom 52
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nr 1
EN
Agrafeuil and Zarrabi in [1] characterized all closed ideals with at most countable hull in a unital Banach algebra embedded in the classical disc algebra and satisfying certain conditions ((H1), (H2), (H3)), and the analytic Ditkin condition. We modify Ditkin’s condition and show that analogous result is true for a wider class of algebras. This is an extension of the result obtained in [1].
2
Content available remote

The continuity of Lie homomorphisms

100%
Aupetit B., Mathieu M.
Studia Mathematica
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2000
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tom 138
|
nr 2
193-199
EN
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
3
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Minimal incomplete norms on Banach algebras

100%
Meyer M. J.
Studia Mathematica
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1992
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tom 102
|
nr 1
77-85
EN
We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
4
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Inequalities Of Lipschitz Type For Power Series In Banach Algebras

100%
Dragomir S. S.
Annales Mathematicae Silesianae
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2015
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tom 29
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nr 1
61-83
EN
Let [...] f(z)=∑n=0∞αnzn $f(z) = \sum\nolimits_{n = 0}^\infty {\alpha _n z^n }$ be a function defined by power series with complex coefficients and convergent on the open disk D (0, R) ⊂ ℂ, R > 0. For any x, y ∈ ℬ, a Banach algebra, with ‖x‖, ‖y‖ < R we show among others that [...] ‖f(y)−f(x)‖≤‖y−x‖∫01fa′(‖(1−t)x+ty‖)dt $$\left\| {f(y) - f(x)} \right\| \le \left\| {y - x} \right\|\int_0^1 {f_a^\prime } (\left\| {(1 - t)x + ty} \right\|)dt$$ where [...] fa(z)=∑n=0∞|αn| zn $f_a (z) = \sum\nolimits_{n = 0}^\infty {|\alpha _n |} \;z^n$ . Inequalities for the commutator such as [...] ‖f(x)f(y)−f(y)f(x)‖≤2fa(M)fa′(M)‖y−x‖, $$\left\| {f(x)f(y) - f(y)f(x)} \right\| \le 2f_a (M)f_a^\prime (M)\left\| {y - x} \right\|,$$ if ‖x‖, ‖y‖ ≤ M < R, as well as some inequalities of Hermite–Hadamard type are also provided.
5
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Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

63%
Abbas S., Benchohra M., Abdalla Darwish M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2016
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tom 36
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nr 2
155-179
EN
In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
6
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An asymptotic expansion for the distribution of the supremum of a random walk

63%
Sgibnev M. S.
Studia Mathematica
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2000
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tom 140
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nr 1
41-55
EN
Let ${S_n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of ${S_n}$ which takes into account the influence of the roots of the equation $1-∫_ℝe^{sx}F(dx)=0,F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms.
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