In this work, we give some topological properties of the sequence spaces <InlineEquation ID="IEq2"><EquationSource Format="MATHML"><math><msub><mi>ℓ</mi><mi>p</mi></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$\ell _{p}(\widehat{B}_{q})$</EquationSource></InlineEquation> (with <InlineEquation ID="IEq3"><EquationSource Format="MATHML"><math><mn>0</mn><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></EquationSource><EquationSource Format="TEX">$0< p<1$</EquationSource></InlineEquation>), <InlineEquation ID="IEq4"><EquationSource Format="MATHML"><math><msub><mi>c</mi><mn>0</mn></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$c_{0}(\widehat{B}_{q})$</EquationSource></InlineEquation>, <InlineEquation ID="IEq5"><EquationSource Format="MATHML"><math><mi>c</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$c(\widehat{B}_{q})$</EquationSource></InlineEquation>, and <InlineEquation ID="IEq6"><EquationSource Format="MATHML"><math><msub><mi>ℓ</mi><mi mathvariant="normal">∞</mi></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$\ell _{\infty }(\widehat{B}_{q})$</EquationSource></InlineEquation> defined by the matrix <InlineEquation ID="IEq7"><EquationSource Format="MATHML"><math><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub></math></EquationSource><EquationSource Format="TEX">$\widehat{B}_{q}$</EquationSource></InlineEquation>. Furthermore, we construct bases for the space <InlineEquation ID="IEq8"><EquationSource Format="MATHML"><math><msub><mi>c</mi><mn>0</mn></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$c_{0}(\widehat{B}_{q})$</EquationSource></InlineEquation> and <InlineEquation ID="IEq9"><EquationSource Format="MATHML"><math><mi>c</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$c(\widehat{B}_{q})$</EquationSource></InlineEquation>, determine α-, β-, γ-duals of the above defined spaces, classify some matrix classes and provide several results related to compactness of certain matrix operators on the space <InlineEquation ID="IEq10"><EquationSource Format="MATHML"><math><msub><mi>c</mi><mn>0</mn></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>B</mi><mo>ˆ</mo></mover><mi>q</mi></msub><mo stretchy="false">)</mo></math></EquationSource><EquationSource Format="TEX">$c_{0}(\widehat{B}_{q})$</EquationSource></InlineEquation>.

Some q-Bell sequence spaces associated with c and $c_{0}$

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2026年6月15日

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Koray İbrahim Atabey,
Taja Yaying,
Mikail Et

摘要

In this work, we give some topological properties of the sequence spaces $ℓ_{p} ({\hat{B}}_{q})$ $\ell _{p}(\widehat{B}_{q})$ (with $0 < p < 1$ $0< p<1$), $c_{0} ({\hat{B}}_{q})$ $c_{0}(\widehat{B}_{q})$, $c ({\hat{B}}_{q})$ $c(\widehat{B}_{q})$, and $ℓ_{\infty} ({\hat{B}}_{q})$ $\ell _{\infty }(\widehat{B}_{q})$ defined by the matrix ${\hat{B}}_{q}$ $\widehat{B}_{q}$. Furthermore, we construct bases for the space $c_{0} ({\hat{B}}_{q})$ $c_{0}(\widehat{B}_{q})$ and $c ({\hat{B}}_{q})$ $c(\widehat{B}_{q})$, determine α-, β-, γ-duals of the above defined spaces, classify some matrix classes and provide several results related to compactness of certain matrix operators on the space $c_{0} ({\hat{B}}_{q})$ $c_{0}(\widehat{B}_{q})$.

Some q-Bell sequence spaces associated with c and \(c_{0}\)

摘要