Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Generalized Difference Matrix Domain on Strongly Almost
  Convergent Double Sequence Spaces   Most recently, some new double sequence spaces $B(\mathcal{M}_{u})$,
$B(\mathcal{C}_{\vartheta})$ where $\vartheta=\{b,bp,r,f,f_0\}$ and
$B(\mathcal{L}_{q})$ for $0<q<\infty$ have been introduced as four-dimensional
generalized difference matrix $B(r,s,t,u)$ domain on the double sequence spaces
$\mathcal{M}_{u}$, $\mathcal{C}_{\vartheta}$ where $\vartheta=\{b,bp,r,f,f_0\}$
and $\mathcal{L}_{q}$ for $0<q<\infty$, and some topological properties, dual
spaces, some new four-dimensional matrix classes and matrix transformations
related to these spaces have also been studied by Tu\u{g} and Ba\c{s}ar and
Tu\u{g} (see \cite{OT,OT2,Orhan,Orhan 2}). In this present paper, we introduce
new strongly almost null and strongly almost convergent double sequence spaces
$B[\mathcal{C}_f]$ and $B[\mathcal{C}_{f_0}]$ as domain of four-dimensional
generalized difference matrix $B(r,s,t,u)$ in the spaces $[\mathcal{C}_f]$ and
$[\mathcal{C}_{f_0}]$, respectively. Firstly, we prove that the new double
sequence spaces $B[\mathcal{C}_f]$ and $B[\mathcal{C}_{f_0}]$ are Banach spaces
with its norm. Then, we give some inclusion relations including newly defined
strongly almost convergent double sequence spaces. Moreover, we calculate the
$\alpha-$dual, $\beta(bp)-$dual and $\gamma-$dual of the space
$B[\mathcal{C}_f]$. Finally, we characterize new four-dimensional matrix
classes $([\mathcal{C}_{f}];\mathcal{C}_{f})$,
$([\mathcal{C}_{f}];\mathcal{M}_{u})$, $(B[\mathcal{C}_{f}];\mathcal{C}_{f})$,
$(B[\mathcal{C}_{f}];\mathcal{M}_{u})$ and we complete this work with some
significant results.

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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat