Corrigendum to “Tautness for sets of multiples and applications to $\mathcal B$-free dynamics” (Studia Math. 247 (2019), 205–216)

2021 ◽  
Vol 258 (2) ◽  
pp. 235-237
Author(s):  
Gerhard Keller
Keyword(s):  
Studia Math

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

scholarly journals ON λ-STRICT IDEALS IN BANACH SPACES

2010 ◽  
Vol 83 (2) ◽  
pp. 231-240 ◽  
Author(s):  
TROND A. ABRAHAMSEN ◽  
OLAV NYGAARD
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Studia Math ◽  
Separable Case ◽  
Baire One ◽  
Ideal Property ◽  
Open Question

AbstractWe define and study λ-strict ideals in Banach spaces, which for λ=1 means strict ideals. Strict u-ideals in their biduals are known to have the unique ideal property; we prove that so also do λ-strict u-ideals in their biduals, at least for λ>1/2. An open question, posed by Godefroy et al. [‘Unconditional ideals in Banach spaces’, Studia Math.104 (1993), 13–59] is whether the Banach space X is a u-ideal in Ba(X), the Baire-one functions in X**, exactly when κu(X)=1; we prove that if κu(X)=1 then X is a strict u-ideal in Ba (X) , and we establish the converse in the separable case.

scholarly journals Remark on our paper ``On bases in Banach spaces'' (Studia Math. 170 (2005), 147–171)

2009 ◽  
Vol 191 (2) ◽  
pp. 201
Author(s):  
T. Bartoszyński ◽  
M. Džamonja ◽  
L. Halbeisen ◽  
E. Murtinová ◽  
A. Plichko
Keyword(s):  
Banach Spaces ◽  
Studia Math

scholarly journals Invariant vector means and complementability of Banach spaces in their second duals

2022 ◽  
Author(s):  
Radosław Łukasik
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Studia Math ◽  
Cancellative Semigroup ◽  
Invariant Mean ◽  
Invariant Vector ◽  
Free Rank ◽  
Torsion Free Rank ◽  
Torsion Free

AbstractLet X be a Banach space. Fix a torsion-free commutative and cancellative semigroup S whose torsion-free rank is the same as the density of $$X^{**}$$ X ∗ ∗ . We then show that X is complemented in $$X^{**}$$ X ∗ ∗ if and only if there exists an invariant mean $$M:\ell _\infty (S,X)\rightarrow X$$ M : ℓ ∞ ( S , X ) → X . This improves upon previous results due to Bustos Domecq (J Math Anal Appl 275(2):512–520, 2002), Kania (J Math Anal Appl 445:797–802, 2017), Goucher and Kania (Studia Math 260:91–101, 2021).

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