Uniqueness of unconditional basis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">T</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>⊕</mml:mo><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/…
نویسندگان
چکیده
Our goal in this paper is to advance the state of art topic uniqueness unconditional basis. To that end we establish general conditions on a pair (X,Y) formed by quasi-Banach space X and Banach Y which guarantee every basis their direct sum X⊕Y splits into bases each summand. As application our methods obtain that, among others, spaces Hp(Td)⊕T(2) Hp(Td)⊕ℓ2, for p∈(0,1) d∈N, have unique (up equivalence permutation).
منابع مشابه
Uniqueness of Unconditional Bases in Banach Spaces
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2022.109597