TY - JOUR AU - OLSZOWY, LESZEK PY - 2021/05/16 Y2 - 2024/03/29 TI - LOCAL AND UNIFORM NEAR SMOOTHNESS OF SOME BANACH SPACES JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 28 IS - 4 SE - Papers DO - 10.5556/j.tkjm.28.1997.4247 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4247 SP - 253-263 AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: -3.000000pt;">In this paper we </span><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: -3.000000pt;">g</span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">ive an estimate of the modulus o</span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: 4.000000pt;">f near smoothness of the space $<span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: 6.000000pt;">c_o(E_i)$. In the case of the space&nbsp;</span><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: 6.000000pt;">$<span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT'; vertical-align: 6.000000pt;">c_o(l_{p_i})$</span> <span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';"> the exact formula for this modulus is derived. Moreover, we show that the properties of </span></span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';"> near uniform smoothness and local near uniform smoothness are hereditary with respect to the product space $c_o(E_i)$.</span></span></p></div></div><div class="layoutArea"><div class="column"><p><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">&nbsp;</span></p></div></div></div> ER -