Complexity of weakly null sequences

We introduce an ordinal index which measures the complexity of a weakly null sequence, and show that a construction due to J. Schreier can be iterated to produce for each alpha < omega_1, a weakly null sequence (x^{alpha}_n)_n in C(omega^{omega^{alpha}})) with complexity alpha. As in the Schreier example each of these is a sequence of indicator functions which is a suppression-1 unconditional basic sequence. These sequences are used to construct Tsirelson-like spaces of large index. We also show that this new ordinal index is related to the Lavrentiev index of a Baire-1 function and use the index to sharpen some results of Alspach and Odell on averaging weakly null sequences

Ursinus College Alumni Journal, Winter 1942

Current comment: Loyalty fund • President\u27s letter • College is recipient of new hymnals for chapel • Opening of 73rd academic year: Student enrollment above last year\u27s figures; Pfahler Hall dedicated at annual Founders Day • Chester Robbins gets high position in New Jersey • Athletics for all is aim of war training program • Hendricks and Kepler pass away: Loyal Ursinus alumni • Some of our alumni in U. S. N. • Ursinus graduates elected to legislative posts • Ursinusites, at home and abroad • Alumni serving with the colors • Alumni Association officershttps://digitalcommons.ursinus.edu/alumnijournal/1016/thumbnail.jp

Ursinus College Alumni Journal, Summer 1942

Current comment: Ursinus at war; Lieutenant Aram Y. Parunak, U. S. N., \u2733; Prospective students and the Selective Service • President\u27s page • 72nd annual commencement • Miss Ermold retires • Summer session draws larger registration • New Selective Service deferment for students • Dr. Reginald Sibbald passes away • Dr. Yost mourned by grads and students • Ursinus director passes • Our alumni secretary\u27s page • New changes in administrative posts • Local alumni group meetings • Report on your funds • Ursinusites, at home and abroad • Our service men • 1942 varsity football schedulehttps://digitalcommons.ursinus.edu/alumnijournal/1015/thumbnail.jp