The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces
Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1586 |
| _version_ | 1797503789940342784 |
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| author | Ju Myung Kim |
| author_facet | Ju Myung Kim |
| author_sort | Ju Myung Kim |
| collection | DOAJ |
| description | Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>≤</mo><mo>∞</mo></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>p</mi><mo>+</mo><mn>1</mn><mo>/</mo><mi>q</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula>) be the ideal of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-compact operators. This paper investigates the compactness and null sequences via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula>, and an approximation property of the ideal of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula>-compact operators. |
| first_indexed | 2024-03-10T03:55:22Z |
| format | Article |
| id | doaj.art-2669a3019ea841c1a0646a0f2c6666e4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:55:22Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2669a3019ea841c1a0646a0f2c6666e42023-11-23T08:46:32ZengMDPI AGMathematics2227-73902022-05-01109158610.3390/math10091586The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach SpacesJu Myung Kim0Department of Mathematics and Statistics, Sejong University, Seoul 05006, KoreaLet <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>≤</mo><mo>∞</mo></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>p</mi><mo>+</mo><mn>1</mn><mo>/</mo><mi>q</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula>) be the ideal of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-compact operators. This paper investigates the compactness and null sequences via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula>, and an approximation property of the ideal of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></semantics></math></inline-formula>-compact operators.https://www.mdpi.com/2227-7390/10/9/1586compact setnull sequence(<i>p</i>,<i>q</i>)-compact operatorBanach operator idealapproximation property |
| spellingShingle | Ju Myung Kim The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces Mathematics compact set null sequence (<i>p</i>,<i>q</i>)-compact operator Banach operator ideal approximation property |
| title | The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces |
| title_full | The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces |
| title_fullStr | The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces |
| title_full_unstemmed | The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces |
| title_short | The <i>K</i><sub><i>p</i>,<i>q</i></sub>-Compactness and <i>K</i><sub><i>p</i>,<i>q</i></sub>-Null Sequences, and the <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">K</mi><mrow><msub><mi mathvariant="bold-italic">K</mi><mrow><mi mathvariant="bold-italic">p</mi><mo>,</mo><mi mathvariant="bold-italic">q</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>-Approximation Property for Banach Spaces |
| title_sort | i k i sub i p i i q i sub compactness and i k i sub i p i i q i sub null sequences and the inline formula math display inline semantics mrow msub mi mathvariant bold script k mi mrow msub mi mathvariant bold italic k mi mrow mi mathvariant bold italic p mi mo mo mi mathvariant bold italic q mi mrow msub mrow msub mrow semantics math inline formula approximation property for banach spaces |
| topic | compact set null sequence (<i>p</i>,<i>q</i>)-compact operator Banach operator ideal approximation property |
| url | https://www.mdpi.com/2227-7390/10/9/1586 |
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