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257 10 |
Ultima descărcare din IBN: 2024-01-03 02:58 |
Căutarea după subiecte similare conform CZU |
517.98 (48) |
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (241) |
SM ISO690:2012 GOK, Omer. On regular operators on Banach Lattices. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2022, nr. 2(14), pp. 53-56. ISSN 2537-6284. DOI: https://doi.org/10.36120/2587-3644.v14i2.53-56 |
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Acta et commentationes (Ştiinţe Exacte și ale Naturii) | |||||
Numărul 2(14) / 2022 / ISSN 2537-6284 /ISSNe 2587-3644 | |||||
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DOI: https://doi.org/10.36120/2587-3644.v14i2.53-56 | |||||
CZU: 517.98 | |||||
MSC 2010: 46B25, 46B42, 47B60, 47B65. | |||||
Pag. 53-56 | |||||
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Let $E$ and $F$ be Banach lattices and $X$ and $Y$ be Banach spaces. A linear operator$T: E \rightarrow F$ is called regular if it is the difference of two positive operators. $L_{r}(E,F)$ denotes the vector space of all regular operators from $E$ into $F$. A continuous linear operator $T: E \rightarrow X$ is called $M$-weakly compact operator if for every disjoint bounded sequence $(x_{n})$ in $E$, we have $lim_{n \rightarrow\infty} \| Tx_{n} \| =0$. $W^{r}_{M}(E,F)$ denotes the regular $M$-weakly compact operators from $E$ into $F$. This paper is devoted to the study of regular operators and $M$-weakly compact operators on Banach lattices. We show that $F$ has a b-property if and only if $L_{r}(E,F)$ has b-property. Also, $W^{r}_{M}(E,F)$ is a $KB$-space if and only if $F$ is a $KB$-space. |
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Cuvinte-cheie Banach lattice, regular operators, M-weakly compact operators, order continuous norm, latice Banach, operatori regulari, operatori M-slab compacți, norma continue de ordine |
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