It seems that nobody has opened here the theme of the posterity of Byzantium. Here are three classics, untill now unsurpassed. Historians are still working in their paradigm.
The first is the Russian historian A. P. Lebedev, "История Греко-восточной церкви под властью турок. От падения Константинополя (в 1453 году) до настоящего времени", 1908, 2 volumes. It seems there is a new edition in Skt. Petersburg, 2004. Excellent documentation, pervasive critical spirit, but maybe not too philhellenical, as the spirit was going in his time.
The second is the Romanian scholar Nicolae Iorga, "Byzance apres Byzance. Continuation de l'Histoire de la vie byzantine", Bucarest, 1935. This is a real wind of change, a truly innovative model of understanding the post-byzantine reality. One can hardly find a work which don't make (at least a) ritual reference to the "Byzantium after Byzantium" concept. But maybe the whole work is less read, and that's too bad.
The third is the British well known historian Sir Steven Runciman, "The Great Church in Captivity. A study of the Patriarchate of Constantinople from the eve of the Turkish conquest to the Greek War of Independence", 1968, yet another milestone in the field. A good breath of philhellenic mood, in order to gloriously accomplish the present trilogy.
All in just one-click.
http://mihd.net/sik4xv See also
N. IORGA - Histoire de la vie byzantine - EMPIRE ET CIVILISATION - D'APRES LES SOURCES ILLUSTREE PAR LES MONNAIES- I. L'Empire oecumenique (527 - 641)
http://www.unibuc.ro/CLASSICA/iorga1/index.htm N. IORGA - Histoire de la vie byzantine - EMPIRE ET CIVILISATION - D'APRES LES SOURCES - ILLUSTRÉE PAR LES MONNAIES- II. L'Empire moyen de civilisation hellenique (641 - 1081)
http://www.unibuc.ro/CLASSICA/iorga2/index.htm N. IORGA - Histoire de la vie byzantine - EMPIRE ET CIVILISATION - D'APRES LES SOURCES ILLUSTREE PAR LES MONNAIES - III. L'Empire de penetration latine (1081 - 1453)
http://www.unibuc.ro/CLASSICA/iorga3/index.htm