On weakly $\theta $-continuous functions

F. Commaroto; T. Noiri

Displaying similar documents to “On weakly $θ$ -continuous functions”

On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

Agnieszka Kałamajska (2001)

Colloquium Mathematicae

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We study the functional $I_{f} (u) = \int_{Ω} f (u (x)) d x$ , where u=(u₁, ..., uₘ) and each $u_{j}$ is constant along some subspace $W_{j}$ of ℝⁿ. We show that if intersections of the $W_{j}$ ’s satisfy a certain condition then $I_{f}$ is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on ${W_{j}}_{j = 1, . . ., m}$ to have the equivalence: $I_{f}$ is weakly continuous if and only if f is Λ-affine.

Weak precompactness and property (V*) in spaces of compact operators

Ioana Ghenciu (2015)

Colloquium Mathematicae

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We give sufficient conditions for subsets of compact operators to be weakly precompact. Let $L_{w *} (E *, F)$ (resp. $K_{w *} (E *, F)$ ) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F. We prove that if H is a subset of $K_{w *} (E *, F)$ such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results: If E has property (wV*) and F has property (V*), then $K_{w *} (E *, F)$ has property (wV*). Suppose...

Characterizing matrices with $𝐗$ -simple image eigenspace in max-min semiring

Ján Plavka, Sergeĭ Sergeev (2016)

Kybernetika

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A matrix $A$ is said to have $𝐗$ -simple image eigenspace if any eigenvector $x$ belonging to the interval $𝐗 = {x : \underset{̲}{x} \leq x \leq \bar{x}}$ is the unique solution of the system $A \otimes y = x$ in $𝐗$ . The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability)...

Factorizations of normality via generalizations of $β$ -normality

Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)

Mathematica Bohemica

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The notion of $β$ -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost $β$ -normal spaces, which is a simultaneous generalization of $β$ -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak $β$ -normality, in terms of $θ$ -closed sets, which turns out to be a simultaneous generalization of $β$ -normality and $θ$ -normality. A space $X$ is said to be weakly $β$ -normal (w $β$ -normal $)$ if for every...

Some remarks on the interpolation spaces $A^{θ}, A_{θ}$

Mohammad Daher (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let $(A_{0}, A_{1})$ be a regular interpolation couple. Under several different assumptions on a fixed $A^{β}$ , we show that $A^{θ} = A_{θ}$ for every $θ \in (0, 1)$ . We also deal with assumptions on ${\bar{A}}^{β}$ , the closure of $A^{β}$ in the dual of ${(A_{0}^{*}, A_{1}^{*})}_{β}$ .

The subspace of weak $P$ -points of $ℕ^{*}$

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let $W$ be the subspace of $ℕ^{*}$ consisting of all weak $P$ -points. It is not hard to see that $W$ is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that $W$ is a $p$ -pseudocompact space for all $p \in ℕ^{*}$ .

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

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Seeds of sunflowers are often modelled by $n ⟼ ϕ_{θ} (n) = \sqrt{n} e^{2 i π n θ}$ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance $2 π θ$ for $θ$ the golden ratio. We associate to such a map $ϕ_{θ}$ a geodesic path $γ_{θ} : ℝ_{> 0} ⟶ {PSL}_{2} (ℤ) ∖ ℍ$ of the modular curve and use it for local descriptions of the image $ϕ_{θ} (ℕ)$ of the phyllotactic map $ϕ_{θ}$ .

Singularities of $2 Θ$ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

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We consider the linear system $| 2 Θ_{0} |$ of second order theta functions over the Jacobian $J C$ of a non-hyperelliptic curve $C$ . A result by J.Fay says that a divisor $D \in | 2 Θ_{0} |$ contains the origin $𝒪 \in J C$ with multiplicity $4$ if and only if $D$ contains the surface $C - C = {𝒪 (p - q) ∣ p, q \in C} \subset J C$ . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing $𝒪$ with multiplicity $6$ , divisors containing the fourfold $C_{2} - C_{2} = {𝒪 (p + q - r - s) ∣ p, q, r, s \in C}$ , and divisors singular along $C - C$ , using...

The Lindelöf property in Banach spaces

B. Cascales, I. Namioka, J. Orihuela (2003)

Studia Mathematica

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A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space $M^{D}$ the following four conditions are equivalent: (i) K is fragmented by $d_{D}$ , where, for each S ⊂ D, $d_{S} (x, y) = s u p ϱ (x (t), y (t)) : t \in S$ . (ii) For each countable subset...

Compatibility of the theta correspondence with the Whittaker functors

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

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We prove that the global geometric theta-lifting functor for the dual pair $(H, G)$ is compatible with the Whittaker functors, where $(H, G)$ is one of the pairs $({S 𝕆}_{2 n}, {𝕊 p}_{2 n})$ , $({𝕊 p}_{2 n}, {S 𝕆}_{2 n + 2})$ or $({𝔾 L}_{n}, {𝔾 L}_{n + 1})$ . That is, the composition of the theta-lifting functor from $H$ to $G$ with the Whittaker functor for $G$ is isomorphic to the Whittaker functor for $H$ .

Weakly null sequences with upper estimates

Daniel Freeman (2008)

Studia Mathematica

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We prove that if $(v_{i})$ is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_{i})$ , then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_{i})$ . This extends a result of Knaust and Odell, who proved this for the cases in which $(v_{i})$ is the standard basis for $ℓ_{p}$ or c₀.

Property $(𝐰𝐋)$ and the reciprocal Dunford-Pettis property in projective tensor products

Ioana Ghenciu (2015)

Commentationes Mathematicae Universitatis Carolinae

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A Banach space $X$ has the reciprocal Dunford-Pettis property ( $R D P P$ ) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $R D P P$ (resp. property $(w L)$ ) if every $L$ -subset of $X^{*}$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes_{π} Y$ has property $(w L)$ when $X$ has the $R D P P$ , $Y$ has property $(w L)$ , and $L (X, Y^{*}) = K (X, Y^{*})$ .

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The extremal functions $f_{0} (z)$ realizing the maxima of some functionals (e.g. $max | a_{3} |$ , and $max a r g f^{^{'}} (z)$ ) within the so-called universal linearly invariant family $U_{α}$ (in the sense of Pommerenke [10]) have such a form that $f_{0}^{^{'}} (z)$ looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials $P_{n}^{λ} (x; θ, ψ)$ of a real variable $x$ as coefficients of $G^{λ} (x; θ, ψ; z) = \frac{1}{{(1 - z e^{i θ})}^{λ - i x} {(1 - z e^{i ψ})}^{λ + i x}} = \sum_{n = 0}^{\infty} P_{n}^{λ} (x; θ, ψ) z^{n}, | z | < 1,$ where the parameters $λ$ , $θ$ , $ψ$ satisfy the conditions:...

On ultra-weak convergence in $L^{p}$

Donald E. Myers (1976)

Annales Polonici Mathematici

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The CR Yamabe conjecture the case $n = 1$

Najoua Gamara (2001)

Journal of the European Mathematical Society

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Let $(M, θ)$ be a compact CR manifold of dimension $2 n + 1$ with a contact form $θ$ , and $L = (2 + 2 / n) Δ_{b} + R$ its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form $\tilde{θ}$ on $M$ conformal to $θ$ which has a constant Webster curvature. This problem is equivalent to the existence of a function $u$ such that $L u = u^{1 + 2 / n}$ , $u > 0$ on $M$ . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where $n \geq 2$ and $(M, θ)$ is not locally CR equivalent to the sphere $S^{2 n + 1}$ of $𝐂^{n}$ . In a join work with R. Yacoub, the CR Yamabe...

Comments on the fractional parts of Pisot numbers

Toufik Zaïmi, Mounia Selatnia, Hanifa Zekraoui (2015)

Archivum Mathematicum

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Let $L (θ, λ)$ be the set of limit points of the fractional parts ${λ θ^{n}}$ , $n = 0, 1, 2, \dots$ , where $θ$ is a Pisot number and $λ \in ℚ (θ)$ . Using a description of $L (θ, λ)$ , due to Dubickas, we show that there is a sequence ${(λ_{n})}_{n \geq 0}$ of elements of $ℚ (θ)$ such that $Card (L (θ, λ_{n})) < Card (L (θ, λ_{n + 1}))$ , $\forall$ $n \geq 0$ . Also, we prove that the fractional parts of Pisot numbers, with a fixed degree greater than 1, are dense in the unit interval.

Displaying similar documents to “On weakly θ -continuous functions”

Displaying similar documents to “On weakly $θ$ -continuous functions”