contains every two-dimensional normed space
David Yost (1988)
Annales Polonici Mathematici
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David Yost (1988)
Annales Polonici Mathematici
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Gennadiy Averkov, Horst Martini (2009)
Colloquium Mathematicae
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Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
Teresa Bermúdez, Carlos Díaz Mendoza, Antonio Martinón (2012)
Studia Mathematica
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A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X, . We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if and are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if is an (m,p)-isometry and is an (l,p)-isometry, then is an (h,p)-isometry, where t = gcd(r,s)...
Václav Kryštof (2018)
Commentationes Mathematicae Universitatis Carolinae
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We prove that for a normed linear space , if is continuous and semiconvex with modulus , is continuous and semiconcave with modulus and , then there exists such that . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ) to the case of an arbitrary nontrivial modulus . This generalization (where a function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.
Tord Sjödin (2018)
Czechoslovak Mathematical Journal
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Let be a closed subset of and let denote the metric projection (closest point mapping) of onto in -norm. A classical result of Asplund states that is (Fréchet) differentiable almost everywhere (a.e.) in in the Euclidean case . We consider the case and prove that the th component of is differentiable a.e. if and satisfies Hölder condition of order if .
Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari (2015)
Czechoslovak Mathematical Journal
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Let be a Banach space of analytic functions on the open unit disk and a subset of linear isometries on . Sufficient conditions are given for non-supercyclicity of . In particular, we show that the semigroup of linear isometries on the spaces (), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space or the Bergman space (, )...
F. Dai, Z. Ditzian, Hongwei Huang (2010)
Studia Mathematica
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Suppose Δ̃ is the Laplace-Beltrami operator on the sphere and where ρ ∈ SO(d). Then and are equivalent for 1 < p < ∞. We note that for even m the relation was recently investigated by the second author. The equivalence yields an extension of the results on sharp Jackson inequalities on the sphere. A new strong converse inequality for given in this paper plays a significant role in the proof.
Said Bouali, Youssef Bouhafsi (2015)
Mathematica Bohemica
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Let denote the algebra of operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the elementary operator are defined by and for all . In this paper, we exhibit pairs of operators such that the range-kernel orthogonality of holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of with respect to the wider class of unitarily invariant...
Joseph Kupka
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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the spaces................................. 114. Integral representation of bounded linear functionals on ........ 235. Examples in theory...................................................................................
Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)
Mathematica Bohemica
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Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there...
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
Rajendra K. Sharma, Gaurav Mittal (2022)
Mathematica Bohemica
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We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .
Tomoko Hachiro, Takateru Okayasu (2003)
Studia Mathematica
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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., ), and a linear isometry from M into C(Y) (resp., ). We show, under the assumption that , where is...
Tamás Erdélyi (2001)
Colloquium Mathematicae
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Let D and ∂D denote the open unit disk and the unit circle of the complex plane, respectively. We denote by ₙ (resp. ) the set of all polynomials of degree at most n with real (resp. complex) coefficients. We define the truncation operators Sₙ for polynomials of the form , , by , (here 0/0 is interpreted as 1). We define the norms of the truncation operators by , . Our main theorem establishes the right order of magnitude of the above norms: there is an absolute constant c₁...
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.