Matches in SemOpenAlex for { <https://semopenalex.org/work/W3103463492> ?p ?o ?g. }
- W3103463492 endingPage "6998" @default.
- W3103463492 startingPage "6961" @default.
- W3103463492 abstract "The paper elucidates the relationship between the density of a Banach space and possible sizes of Auerbach systems and well-separated subsets of its unit sphere. For example, it is proved that for a large enough space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the unit sphere <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S Subscript upper X> <mml:semantics> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>S_X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> always contains an uncountable <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis 1 plus right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(1+)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-separated subset. In order to achieve this, new results concerning the existence of large Auerbach systems are established, that happen to be sharp for the class of weakly Lindelöf determined (WLD) spaces. In fact, we offer the first consistent example of a non-separable WLD Banach space that contains no uncountable Auerbach system, as witnessed by a renorming of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c 0 left-parenthesis omega 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>ω<!-- ω --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>c_0(omega _1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Moreover, the following optimal results for the classes of, respectively, reflexive and super-reflexive spaces are established: the unit sphere of an infinite-dimensional reflexive space contains a symmetrically <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis 1 plus epsilon right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε<!-- ε --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(1+varepsilon )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-separated subset of any regular cardinality not exceeding the density of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; should the space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be super-reflexive, the unit sphere of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains such a subset of cardinality equal to the density of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The said problem is studied for other classes of spaces too, including WLD spaces, RNP spaces, or strictly convex ones." @default.
- W3103463492 created "2020-11-23" @default.
- W3103463492 creator A5033512326 @default.
- W3103463492 creator A5036484429 @default.
- W3103463492 creator A5065775612 @default.
- W3103463492 date "2020-08-05" @default.
- W3103463492 modified "2023-10-14" @default.
- W3103463492 title "Separated sets and Auerbach systems in Banach spaces" @default.
- W3103463492 cites W1004592162 @default.
- W3103463492 cites W1040866619 @default.
- W3103463492 cites W1483711189 @default.
- W3103463492 cites W1489871065 @default.
- W3103463492 cites W1516516351 @default.
- W3103463492 cites W1523918473 @default.
- W3103463492 cites W1531605312 @default.
- W3103463492 cites W1532517928 @default.
- W3103463492 cites W1541055144 @default.
- W3103463492 cites W1596385175 @default.
- W3103463492 cites W1945900451 @default.
- W3103463492 cites W1977087565 @default.
- W3103463492 cites W1998341651 @default.
- W3103463492 cites W2004961163 @default.
- W3103463492 cites W2007810353 @default.
- W3103463492 cites W2034127031 @default.
- W3103463492 cites W2040736162 @default.
- W3103463492 cites W2048456113 @default.
- W3103463492 cites W2050504298 @default.
- W3103463492 cites W2061678951 @default.
- W3103463492 cites W2061870379 @default.
- W3103463492 cites W2066891346 @default.
- W3103463492 cites W2067595046 @default.
- W3103463492 cites W2071031811 @default.
- W3103463492 cites W2088160582 @default.
- W3103463492 cites W2091317618 @default.
- W3103463492 cites W2105902717 @default.
- W3103463492 cites W2132031014 @default.
- W3103463492 cites W2134184786 @default.
- W3103463492 cites W2149246969 @default.
- W3103463492 cites W2498059247 @default.
- W3103463492 cites W2506161474 @default.
- W3103463492 cites W2592942135 @default.
- W3103463492 cites W260636276 @default.
- W3103463492 cites W2760192020 @default.
- W3103463492 cites W2768576186 @default.
- W3103463492 cites W2962951582 @default.
- W3103463492 cites W2963507349 @default.
- W3103463492 cites W2963712148 @default.
- W3103463492 cites W2964327434 @default.
- W3103463492 cites W3099427467 @default.
- W3103463492 cites W4206752726 @default.
- W3103463492 cites W4212888075 @default.
- W3103463492 cites W4232853762 @default.
- W3103463492 cites W4252005208 @default.
- W3103463492 cites W4252734642 @default.
- W3103463492 cites W4254060919 @default.
- W3103463492 cites W4256499462 @default.
- W3103463492 cites W605624406 @default.
- W3103463492 cites W765138080 @default.
- W3103463492 cites W910426389 @default.
- W3103463492 cites W933405741 @default.
- W3103463492 doi "https://doi.org/10.1090/tran/8160" @default.
- W3103463492 hasPublicationYear "2020" @default.
- W3103463492 type Work @default.
- W3103463492 sameAs 3103463492 @default.
- W3103463492 citedByCount "6" @default.
- W3103463492 countsByYear W31034634922021 @default.
- W3103463492 countsByYear W31034634922022 @default.
- W3103463492 countsByYear W31034634922023 @default.
- W3103463492 crossrefType "journal-article" @default.
- W3103463492 hasAuthorship W3103463492A5033512326 @default.
- W3103463492 hasAuthorship W3103463492A5036484429 @default.
- W3103463492 hasAuthorship W3103463492A5065775612 @default.
- W3103463492 hasBestOaLocation W31034634921 @default.
- W3103463492 hasConcept C11413529 @default.
- W3103463492 hasConcept C118615104 @default.
- W3103463492 hasConcept C132954091 @default.
- W3103463492 hasConcept C134306372 @default.
- W3103463492 hasConcept C154945302 @default.
- W3103463492 hasConcept C18903297 @default.
- W3103463492 hasConcept C2776321320 @default.
- W3103463492 hasConcept C2777299769 @default.
- W3103463492 hasConcept C33923547 @default.
- W3103463492 hasConcept C41008148 @default.
- W3103463492 hasConcept C70710897 @default.
- W3103463492 hasConcept C86803240 @default.
- W3103463492 hasConceptScore W3103463492C11413529 @default.
- W3103463492 hasConceptScore W3103463492C118615104 @default.
- W3103463492 hasConceptScore W3103463492C132954091 @default.
- W3103463492 hasConceptScore W3103463492C134306372 @default.
- W3103463492 hasConceptScore W3103463492C154945302 @default.
- W3103463492 hasConceptScore W3103463492C18903297 @default.
- W3103463492 hasConceptScore W3103463492C2776321320 @default.
- W3103463492 hasConceptScore W3103463492C2777299769 @default.
- W3103463492 hasConceptScore W3103463492C33923547 @default.
- W3103463492 hasConceptScore W3103463492C41008148 @default.
- W3103463492 hasConceptScore W3103463492C70710897 @default.
- W3103463492 hasConceptScore W3103463492C86803240 @default.
- W3103463492 hasFunder F4320321006 @default.