A NOTE ON WEAK STABILITY OF ε-SOMETRIES ON CERTAIN BANACH SPACES

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Rohman M., Eryılmaz İ.

JOURNAL OF SCIENCE AND ARTS, sa.2, ss.413-420, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.46939/j.sci.arts-23.2-a08
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.413-420
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we will discuss the weak stability of epsilon-isometries on certain Banach spaces. Let f: X -> Y be a standard epsilon-isometry. If Y* is strictly convex, then for any x* is an element of X*, there is phi is an element of Y* that satisfies parallel to phi parallel to r = parallel to x*parallel to, such that vertical bar < x*, x > - vertical bar <= 2r epsilon, x is an element of X. Also, we show that if X and Y are both L-P spaces (1 < p < infinity), f: X -> Y is a standard epsilon-isometry, then there exists a linear operator T:Y -> X with norm 1 such that parallel to Tf(x) - x parallel to <= 2 epsilon, for all x is an element of X.