Although the concept of Kaldellis that puts the Byzantines as Greek-speaking Romans and simply the continuation of the Roman Empire in the east is widely accepted. This lacks historical record and tries to mold the Byzantines through a modern point of view, and not from a realist who strives to position himself in the Byzantine era and think like one of them and this is what history to achieve. a conlcussion pure and well made.
All this together with his famous book "Hellenism in Byzantium" are nothing more than the point of view of a Byzantinist who wants to talk about the Byzantines in crazy and unrealistic ways and that unfortunately the rest of the people tend to accept and embrace this concept due to its simplicity and little interest.
Now I will begin to talk about what in my institution, I and probably all the serious and famous Byzantine schools believe and I will not use information related to a single Byzantinist (Kaldellis) whose arguments are poorly elaborated.
The problem to start with is that Greek is a very context-dependent language although in some cases this makes it easier to find an explanation. But it happens that the evidence and records in which the Byzantines make it clear that they are of "Hellenic blood" from 330 to 1453 are simply abundant and it would take eternities to point them out to each one.
Let's start with the political aspect that according to Kaldellis is "the bastion of Roman culture in Byzantium" and that is that no aspect in the Byzantine empire was saved from being Hellenized, not even its laws and army (and much less the population) that are normally set as strong "characters of Roman culture in Byzantium".
Byzantine laws were not just Roman and that's it. It was a basis of Roman laws heavily influenced by Hellenistic laws and if several people said that from their inception Roman laws were based on Greek ones etc and it is true but in the Hellenistic East they survived successfully until the fall of "hellas" in 1453 due ( and possibly even today) to their extensive integration into the Byzantine political systems of which they were very aware and it was very common to hear a Byzantine consul boast and pride themselves on the Hellenistic and classical Greek political systems born in the Greek-State cities.
And yes, it is true that they were called Romans and their lands Romania or Hellas but under the Roman term there is nothing other than the Greek identity surviving successfully from 330 to our times!
There are phenomenal records of Byzantines putting the term Roman as synonymous with the term Greek and there are even occasions in which they specifically explain that when a Byzantine mentions the term "Romania", he is calling his home "The land of the Romans" but at the same time time "The land of the Greeks / Hellenes" and they specify very clearly that when they speak of the Basileus Romahion (King of the Romans). They are talking about the "King of the Greeks" and so it happens every time the term "Roman" is mentioned until the final fall of the Empire or as they would have called it "The Monarchy of the Romans" and as they would have thought "The Monarchy of the Greeks "and yes. they were just as aware that their empire was the original legacy of the Roman but this did not prevent them from identifying with an independent and phenomenally different state from the Roman in which apart from the fact that the ancient Romans were considered as "others". It was one dominated by Hellenes and Hellenized people and they liked to flaunt it by putting Alexander the Great in stone carvings on the doors of their monasteries, plates, and urging their soldiers to fight like the Macedonian phalanxes against the Turks (there was a formation very similar to the Macedonian phalanx in the empire and even King Nikephoros is aware of the similarity with these as his book attests) and putting meanders in his shields next to suns of Vergina that symbolized his Christian religion (Vrigen Maria) and his culture Greek at the same time. Or you can also find the Macedonian brigades together with the brigade of the "Companions" that were created by the Byzantines in honor of their ancient Greek history and more examples like this are attested throughout their history but I cannot mention them for their phenomenal abundance. ! it is impossible.
I heartily advise you to read "The history of the Greek nation" by Constantine Paparigopulos.