On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights
Let <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo><</mo> <mi>a</mi> <mo><</mo> <mi>b</mi> <mo><</mo> <mi>c</mi> <mo><&l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-02-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/7/2/212 |
| _version_ | 1831789822004428800 |
|---|---|
| author | Chunji Li Cheon Seoung Ryoo |
| author_facet | Chunji Li Cheon Seoung Ryoo |
| author_sort | Chunji Li |
| collection | DOAJ |
| description | Let <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo><</mo> <mi>a</mi> <mo><</mo> <mi>b</mi> <mo><</mo> <mi>c</mi> <mo><</mo> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> <mo>:</mo> <mo>=</mo> <msup> <mfenced separators="" open="(" close=")"> <mn>1</mn> <mo>,</mo> <msqrt> <mi>a</mi> </msqrt> <mo>,</mo> <msqrt> <mi>b</mi> </msqrt> <mo>,</mo> <msqrt> <mi>c</mi> </msqrt> <mo>,</mo> <msqrt> <mi>d</mi> </msqrt> </mfenced> <mo>∧</mo> </msup> </mrow> </semantics> </math> </inline-formula> be a weighted sequence that is recursively generated by five weights <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>,</mo> <msqrt> <mi>a</mi> </msqrt> <mo>,</mo> <msqrt> <mi>b</mi> </msqrt> <mo>,</mo> </mrow> </semantics> </math> </inline-formula><inline-formula> <math display="inline"> <semantics> <mrow> <msqrt> <mi>c</mi> </msqrt> <mo>,</mo> <msqrt> <mi>d</mi> </msqrt> </mrow> </semantics> </math> </inline-formula>. In this paper, we give sufficient conditions for the positive quadratic hyponormalities of <inline-formula> <math display="inline"> <semantics> <msub> <mi>W</mi> <mrow> <mi>α</mi> <mfenced open="(" close=")"> <mi>x</mi> </mfenced> </mrow> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>W</mi> <mrow> <mi>α</mi> <mfenced separators="" open="(" close=")"> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mfenced> </mrow> </msub> </semantics> </math> </inline-formula>, with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mfenced open="(" close=")"> <mi>x</mi> </mfenced> <mo>:</mo> <msqrt> <mi>x</mi> </msqrt> <mo>,</mo> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mfenced separators="" open="(" close=")"> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mfenced> <mo>:</mo> <msqrt> <mi>y</mi> </msqrt> <mo>,</mo> <msqrt> <mi>x</mi> </msqrt> <mo>,</mo> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> |
| first_indexed | 2024-12-22T14:19:17Z |
| format | Article |
| id | doaj.art-fad42332d2af4a62914f4a52013b84f9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-22T14:19:17Z |
| publishDate | 2019-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fad42332d2af4a62914f4a52013b84f92022-12-21T18:23:02ZengMDPI AGMathematics2227-73902019-02-017221210.3390/math7020212math7020212On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five WeightsChunji Li0Cheon Seoung Ryoo1Department of Mathematics, Northeastern University, Shenyang 110-004, ChinaDepartment of Mathematics, Hannam University, Daejeon 34430, KoreaLet <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo><</mo> <mi>a</mi> <mo><</mo> <mi>b</mi> <mo><</mo> <mi>c</mi> <mo><</mo> <mi>d</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> <mo>:</mo> <mo>=</mo> <msup> <mfenced separators="" open="(" close=")"> <mn>1</mn> <mo>,</mo> <msqrt> <mi>a</mi> </msqrt> <mo>,</mo> <msqrt> <mi>b</mi> </msqrt> <mo>,</mo> <msqrt> <mi>c</mi> </msqrt> <mo>,</mo> <msqrt> <mi>d</mi> </msqrt> </mfenced> <mo>∧</mo> </msup> </mrow> </semantics> </math> </inline-formula> be a weighted sequence that is recursively generated by five weights <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>,</mo> <msqrt> <mi>a</mi> </msqrt> <mo>,</mo> <msqrt> <mi>b</mi> </msqrt> <mo>,</mo> </mrow> </semantics> </math> </inline-formula><inline-formula> <math display="inline"> <semantics> <mrow> <msqrt> <mi>c</mi> </msqrt> <mo>,</mo> <msqrt> <mi>d</mi> </msqrt> </mrow> </semantics> </math> </inline-formula>. In this paper, we give sufficient conditions for the positive quadratic hyponormalities of <inline-formula> <math display="inline"> <semantics> <msub> <mi>W</mi> <mrow> <mi>α</mi> <mfenced open="(" close=")"> <mi>x</mi> </mfenced> </mrow> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>W</mi> <mrow> <mi>α</mi> <mfenced separators="" open="(" close=")"> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mfenced> </mrow> </msub> </semantics> </math> </inline-formula>, with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mfenced open="(" close=")"> <mi>x</mi> </mfenced> <mo>:</mo> <msqrt> <mi>x</mi> </msqrt> <mo>,</mo> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mfenced separators="" open="(" close=")"> <mi>y</mi> <mo>,</mo> <mi>x</mi> </mfenced> <mo>:</mo> <msqrt> <mi>y</mi> </msqrt> <mo>,</mo> <msqrt> <mi>x</mi> </msqrt> <mo>,</mo> <msub> <mover accent="true"> <mi>α</mi> <mo>^</mo> </mover> <mfenced open="[" close="]"> <mn>5</mn> </mfenced> </msub> <mo>.</mo> </mrow> </semantics> </math> </inline-formula>https://www.mdpi.com/2227-7390/7/2/212positively quadratically hyponormalquadratically hyponormalunilateral weighted shiftrecursively generated |
| spellingShingle | Chunji Li Cheon Seoung Ryoo On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights Mathematics positively quadratically hyponormal quadratically hyponormal unilateral weighted shift recursively generated |
| title | On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights |
| title_full | On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights |
| title_fullStr | On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights |
| title_full_unstemmed | On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights |
| title_short | On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights |
| title_sort | on positive quadratic hyponormality of a unilateral weighted shift with recursively generated by five weights |
| topic | positively quadratically hyponormal quadratically hyponormal unilateral weighted shift recursively generated |
| url | https://www.mdpi.com/2227-7390/7/2/212 |
| work_keys_str_mv | AT chunjili onpositivequadratichyponormalityofaunilateralweightedshiftwithrecursivelygeneratedbyfiveweights AT cheonseoungryoo onpositivequadratichyponormalityofaunilateralweightedshiftwithrecursivelygeneratedbyfiveweights |